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**Term(s):**1997**Results:**26**Sorted by:****Page: 1 2 Next**

**Title:**Prediction Games and Arcing Algorithms**Author(s):**Breiman, Leo; **Date issued:**Dec 1997**Date modified:**revised December 14, 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3h3f (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3h40 (PostScript) **Abstract:**The theory behind the success of adaptive reweighting and combining algorithms (arcing) such as Adaboost (Freund and Schapire
[1995, 1996a]) and others in reducing generalization error has not been well understood. By formulating prediction as a game
where one player makes a selection from instances in the training set and the other a convex linear combination of predictors
from a finite set, existing arcing algorithms are shown to be algorithms for finding good game strategies. The minimax theorem
is an essential ingredient of the convergence proofs. An arcing algorithm is described that converges to the optimal strategy.
A bound on the generalization error for the combined predictors in terms of their maximum error is proven that is sharper
than bounds to date. Schapire et al. [1997] offered an explanation of why Adaboost works in terms of its ability to produce
generally high margins. The empirical comparison of Adaboost to the optimal arcing algorithm shows that their explanation
is not complete.**Keyword note:**Breiman__Leo**Report ID:**504**Relevance:**100

**Title:**The SDE solved by local times of a Brownian excursion or bridge derived from the height profile of a random tree or forest**Author(s):**Pitman, Jim; **Date issued:**Dec 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3h0s (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3h1b (PostScript) **Abstract:**Let $B$ be a standard one-dimensional Brownian motion started at 0. Let $L_(t,v)(|B|)$ be the occupation density of $|B|$
at level $v$ up to time $t$. The distribution of the process of local times $(L_(t,v)(|B|), v \ge 0 )$ conditionally given
$B_t = 0$ and $L_(t,0) (|B|)= \ell$ is shown to be that of the unique strong solution $X$ of the \Ito\ SDE $$ dX_v = \left\(
4 - X_v^2 \left( t - \mbox($\int_0^v X_u du$) \right) ^(-1) \right\) \, dv + 2 \sqrt(X_v) d B_v$$ on the interval $[0,V_t
(X))$,where $V_t(X):= \inf \( v: \int_0^v X_u du = t \)$and $X_v = 0$ for all $v \ge V_t(X)$. This conditioned form of the
Ray-Knight description of Brownian local times arises from study of the asymptotic distribution as $n \te \infty$ and $ 2
k/\sqrt(n) \te \ell$ of the height profile of a uniform rooted random forest of $k$ trees labeled by a set of $n$ elements,
as obtained by conditioning a uniform random mapping of the set to itself to have $k$ cyclic points. The SDE is the continuous
analog of a simple description of a Galton-Watson branching process conditioned on its total progeny. A result is obtained
regarding the weak convergence of normalizations of such conditioned Galton-Watson processes and height profiles of random
forests to a solution of the SDE. For $\ell = 0$, corresponding to asymptotics of a uniform random tree, the SDE gives a
new description of the process of local times of a Brownian excursion, implying Jeulin's description of these local times
as a time change of twice a Brownian excursion. Another corollary is the Biane-Yor description of the local times of a reflecting
Brownian bridge as a time changed reversal of twice a Brownian meander of the same length.**Pub info:**Ann. Prob. 27, 261-283 (1999)**Keyword note:**Pitman__Jim**Report ID:**503**Relevance:**100

**Title:**Random spanning trees of Cayley graphs and an associated compactification of semigroups**Author(s):**Evans, S. N.; **Date issued:**Dec 1997**Date modified:**revised March 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3f5h (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3f62 (PostScript) **Abstract:**A sequential construction of a random spanning tree for the Cayley graph of a finitely generated, countably infinite subsemigroup
$V$ of a group $G$ is considered. At stage $n$, the spanning tree $T$ is approximated by a finite tree $T_n$ rooted at the
identity. The approximation $T_(n+1)$ is obtained by connecting edges to the points of $V$ that are not already vertices
of $T_n$ but can be obtained from vertices of $T_n$ via multiplication by a random walk step taking values in the generating
set of $V$. This construction leads to a compactification of the semigroup $V$ in which a sequence of elements of $V$ that
is not eventually constant is convergent if the random geodesic through the spanning tree $T$ that joins the identity to the
$n^(\mathrm th)$ element of the sequence converges in distribution as $n \rightarrow \infty$. The compactification is identified
in a number of examples. Also, it is shown that if $h(T_n)$ and $\#(T_n)$ denote, respectively, the height and size of the
approximating tree $T_n$, then there are constants $0 < c_h \le 1$ and $0 \le c_\# \le \log 2$ such that $\lim_(n \rightarrow
\infty) n^(-1) h(T_n) = c_h$ and $\lim_(n \rightarrow \infty) n^(-1) \log \#(T_n) = c_\#$ almost surely.**Keyword note:**Evans__Steven_N**Report ID:**502**Relevance:**100

**Title:**On Markov Chains with Continuous State Space**Author(s):**Diaconis, Persi; Freedman, David; **Date issued:**Dec 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3d6j (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3d73 (PostScript) **Abstract:**In this expository paper, we prove the following theorem, which may be of some use in studying Markov Chain Monte Carlo methods
like hit and run, the Metropolis algorithm, or the Gibbs sampler. Suppose a discrete-time Markov chain is aperiodic, irreducible,
and there is a stationary probability distribution. Then from almost all starting points the distribution of the chain at
time n converges in norm to the stationary distribution. This known theorem is a special case of more general results due
to Doeblin, and the paper concludes with a brief review of the literature.**Keyword note:**Diaconis__Persi Freedman__David**Report ID:**501**Relevance:**100

**Title:**On the Hit and Run Process**Author(s):**Diaconis, Persi; Freedman, David; **Date issued:**Nov 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3c4x (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3c5g (PostScript) **Abstract:**Given a density f on Euclidean k-space and a starting point x, choose a line L at random through x and move to a point on
L chosen at random from f restricted to L. This procedure defines a Markov chain-- the "hit and run process." The given density
f is stationary; for almost all starting points x, the distribution of the chain at time n converges to the stationary distribution
as n gets large. This expository paper proves some of the convergence theorems, and gives examples.**Keyword note:**Diaconis__Persi Freedman__David**Report ID:**497**Relevance:**100

**Title:**Transforming spatial point processes into Poisson processes**Author(s):**Schoenberg, Frederic; **Date issued:**Nov 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3b06 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3b1r (PostScript) **Abstract:**In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process
of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes,
since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator.
The (F4) condition was removed in 1990 by Nair, but the convexity condition remained. Here both the (F4) condition and the
convexity condition are removed by making use of predictable sets rather than stopping sets. As with Nair's theorem, the
result extends to point processes in higher dimensions.**Keyword note:**Schoenberg__Frederic_R**Report ID:**496**Relevance:**100

**Title:**Coalescents with multiple collisions**Author(s):**Pitman, Jim; **Date issued:**Nov 1997

http://nma.berkeley.edu/ark:/28722/bk0000n381q (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3828 (PostScript) **Abstract:**For each finite measure $\Lambda$ on $[0,1]$, a coalescent Markov process, with state space the compact set of all partitions
of the set $N$ of positive integers, is constructed so the restriction of the partition to each finite subset of $N$ is a
Markov chain with the following transition rates: when the partition has $b$ blocks, each $k$-tuple of blocks is merging to
form a single block at rate $\int_0^1 x^(k-2) (1 - x) ^(b-k) \Lambda(dx)$. Call this process a (\em $\Lambda$-coalescent).
Discrete measure valued processes derived from the $\Lambda$-coalescent model a system of masses undergoing coalescent collisions.
Kingman's coalescent, which has numerous applications in population genetics, is the $\delta_0$-coalescent for $\delta_0$
a unit mass at 0. The coalescent recently derived by Bolthausen and Sznitman from Ruelle's probability cascades, in the context
of the Sherrington-Kirkpatrick spin glass model in mathematical physics, is the $U$-coalescent for $U$ uniform on $[0,1]$.
For $\Lambda=U$, and whenever an infinite number of masses are present, each collision in a $\Lambda$-coalescent involves
an infinite number of masses almost surely, and the proportion of masses involved exists almost surely and is distributed
proportionally to $\Lambda$. The two-parameter Poisson-Dirichlet family of random discrete distributions derived from a
stable subordinator, and corresponding exchangeable random partitions of $N$ governed by a generalization of the Ewens sampling
formula, are applied to describe transition mechanisms for processes of coalescence and fragmentation, including the $U$-coalescent
and its time reversal.**Keyword note:**Pitman__Jim**Report ID:**495**Relevance:**100

**Title:**Geometrically Intrinsic Nonlinear Recursive Filters I: Algorithms**Author(s):**Darling, R. W. R.; **Date issued:**Oct 1997**Date modified:**revised March 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3k7p (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3k87 (PostScript) **Abstract:**The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time
Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different from
the much-used Extended Kalman Filter, and its second-order variants, even in the simplest nonlinear case, in that: * It uses
a quadratic function of a vector observation to update the state, instead of the linear function used by the EKF. * It is
based on deeper geometric principles, which make the GI Filter coordinate-invariant. This implies, for example, that if a
linear system were subjected to a nonlinear transformation f of the state-space and analyzed using the GI Filter, the resulting
state estimates and conditional variances would be the push-forward under f of the Kalman Filter estimates for the untransformed
system -- a property which is not shared by the EKF or its second-order variants. The noise covariance of X and the observation
covariance themselves induce geometries on state space and observation space, respectively, and associated canonical connections.
A sequel to this paper develops stochastic differential geometry results -- based on ``intrinsic location parameters,'' a
notion derived from the heat flow of harmonic mappings -- from which we derive the coordinate-free filter update formula.
The present article presents the algorithm with reference to a specific example -- the problem of tracking and intercepting
a target, using sensors based on a moving missile.**Keyword note:**Darling__R_W_R**Report ID:**494**Relevance:**100

**Title:**Intrinsic Location Parameter of a Diffusion Process**Author(s):**Darling, R. W. R.; **Date issued:**Oct 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3c7k (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3c84 (PostScript) **Abstract:**Suppose $X$ is a Markov diffusion process on $R^p$, or more generally on a manifold $N$. The diffusion variance of $X$ induces
a semi-definite metric $\langle\cdot\mid\cdot\rangle$ on the cotangent bundle, a version of the Levi-Civita connection $\Gamma$
and a Laplace-Beltrami operator $\Delta$. We may treat $X$ as a diffusion on $N$ with generator $\xi + (1/2)\Delta$, where
$\xi$ is a vector field. For sufficiently small $\delta > 0$, $X_\delta$ has an ``intrinsic location parameter'', defined
to be the non-random initial value $V_0$ of a $\Gamma$-martingale $V$ terminating at $X_\delta$. It is obtained by solving
a system of forward-backwards stochastic differential equations (FBSDE): a forward equation for $X$, and a backwards equation
for $V$. This FBSDE is the stochastic equivalent of the heat equation (with drift $\xi$) for harmonic mappings, a well-known
system of quasilinear PDE. Let $\(\phi_t: N \rightarrow N, t \geq 0\)$ be the flow of the vector field $\xi$, and let $x_t
\equiv \phi_t(x_0) \in N$. Our main result is that $\exp^(-1)_(x_\delta)V_0$ can be intrinsically approximated to first order
in $T_(x_\delta)N$ by $$ \nabla d\phi_\delta(x_0)(\Pi_\delta) - \int_(0)^(\delta)(\phi_(\delta - t))_(*)(\nabla d\phi_t(x_0))d\Pi_t
$$ where $\Pi_t = \int_(0)^(t)(\phi_(-s))_(*)\langle\cdot\mid\cdot\rangle_(x_s)ds \in T_(x_0)N \otimes T_(x_0)N$. This is
computed in local coordinates. More generally, we find an intrinsic location parameter for $\Psi(X_\delta)$, if $\Psi:N \rightarrow
M$ is a $C^2$ map into a Riemannian manifold $M$. These formulas have immediate application, discussed in a separate article,
to the construction of an intrinsic nonlinear analog to the Kalman Filter.**Keyword note:**Darling__R_W_R**Report ID:**493**Relevance:**100

**Title:**Collision local times, historical stochastic calculus, and competing superprocesses**Author(s):**Evans, S. N.; Perkins, E. A.; **Date issued:**Sep 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3f85 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3f9q (PostScript) **Abstract:**Branching measure--valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified
by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely
affected by collisions with individuals from the other population. For 3 or fewer spatial dimensions, such processes are
constructed using a new fixed--point technique as the unique solution of a strong equation driven by another pair of more
explicitly constructible measure--valued diffusions. This existence and uniqueness is used to establish well--posedness of
the related martingale problem and hence the strong Markov property for solutions. Previous work of the authors has shown
that in 4 or more dimensions models with the analogous definition do not exist. The definition of the model and its study
require a thorough understanding of random measures called collision local times. These gauge the extent to which two measure--valued
processes or an R^d--valued process and a measure--valued process ``collide'' as time evolves. This study and the substantial
amount of related historical stochastic calculus that is developed are germane to several other problems beyond the scope
of the paper. Moreover, new results are obtained on the branching particle systems imbedded in historical processes and on
the existence and regularity of superprocesses with immigration, and these are also of independent interest.**Keyword note:**Evans__Steven_N Perkins__E_A**Report ID:**491**Relevance:**100

**Title:**Random Brownian Scaling Identities and Splicing of Bessel Processes**Author(s):**Pitman, Jim; Yor, Marc; **Date issued:**Sep 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3g74 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3g8p (PostScript) **Abstract:**An identity in distribution due to F. Knight for Brownian motion is extended in two different ways: firstly by replacing the
supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion, and secondly by replacing the reflecting
Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations
and Brownian excursions. The first extension is related to two different constructions of Ito's law of Brownian excursions,
due to D. Williams and J.-M. Bismut, each involving back-to-back splicing of fragments of two independent three-dimensional
Bessel processes. Generalizations of both splicing constructions are described which involve Bessel processes and Bessel
bridges of arbitrary positive real dimension.**Pub info:**Ann. Prob. 26, 1683-1702 (1998)**Keyword note:**Pitman__Jim Yor__Marc**Report ID:**490**Relevance:**100

**Title:**The Standard Additive Coalescent**Author(s):**Aldous, David; Pitman, Jim; **Date issued:**July 1997**Keyword note:**Aldous__David_J Pitman__Jim**Report ID:**489**Relevance:**100

**Title:**Stationary Markov processes related to stable Ornstein--Uhlenbeck processes and the additive coalescent**Author(s):**Evans, Steven N.; Pitman, Jim; **Date issued:**Jul 1997**Date modified:**revised May 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3r1z (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3r2h (PostScript) **Abstract:**We consider some classes of stationary, counting--measure--valued Markov processes and their companions under time--reversal.
Examples arise in the L\'evy--It\^o decomposition of stable Ornstein--Uhlenbeck processes, the large--time asymptotics of
the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support
of the evolving counting--measure are born or die randomly, but each point follows a deterministic flow during its life--time.**Keyword note:**Evans__Steven_N Pitman__Jim**Report ID:**488**Relevance:**100

**Title:**Interactions among physical and biological variables during the upwelling period in Monterey Bay, CA.**Author(s):**Service, S. K.; Rice, J. A.; Chavez, F. P.; **Date issued:**Jul 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3q89 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3q9v (PostScript) **Abstract:**We used data from moorings deployed in central California to examine the physical variables wind, PAR (photosynthetically
available radiation) and temperature and the biological variable fluorescence during coastal upwelling. Variations of the
multivariate techniques of principal components analysis and canonical correlation were used to extract the major modes of
variability of these variables and to examine relationships among the variables. Data from both 1993 and 1994 indicate a
consistent pattern of relationships among the physical variables, with NW winds and sunnier than average days leading lower
than average temperatures at the mooring by 2-3 days. The relationship among the physical and biological variables was stronger
in 1993 than in 1994. Higher than average fluorescence was found to lag lower than average temperatures, higher than average
PAR and wind from the NW by 4, 6 and 7 days, respectively. The form of the relationship that produced maximal correlation
between fluorescence and temperature was that several days of colder than average temperatures, followed by a trend to increased
temperatures, was correlated with higher than average fluorescence. Higher than average fluorescence in 1993 showed maximal
correlation with wind after several days of NW winds, followed by lighter winds from the SE. Relationships among physical
variables and fluorescence are not as strong in 1994 as in 1993, and we hypothesize these differences to be related to differences
in the strength and duration of upwelling in the two years.**Keyword note:**Service__S_K Rice__John_Andrew Chavez__F_P**Report ID:**487**Relevance:**100

**Title:**Arcing the Edge**Author(s):**Breiman, Leo; **Date issued:**Jun 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3b6h (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3b72 (PostScript) **Abstract:**Recent work has shown that adaptively reweighting the training set, growing a classifier using the new weights, and combining
the classifiers constructed to date can significantly decrease generalization error. Procedures of this type were called
arcing by Breiman [1996]. The first successful arcing procedure was introduced by Freund and Schapire [1995,1996] and called
Adaboost. In an effort to explain why Adaboost works, Schapire, et al [1997] derived a bound on the generalization error
of a convex combination of classifiers in terms of the margin. We introduce a function called the edge, which differs from
the margin only if there are more than two classes. A framework for understanding arcing algorithms is defined. In this
framework, we see that the arcing algorithms currently in the literature are optimization algorithms which minimize some function
of the edge. A relation is derived between the optimal reduction in the maximum value of the and the PAC concept of weak
learner. Two algorithms are described which achieve the optimal reduction. Tests on both synthetic and real data case doubt
on the Schapire, et al explanation.**Keyword note:**Breiman__Leo**Report ID:**486**Relevance:**100

**Title:**Fast evaluation of the likelihood of an HMM: ion channel currents with filtering and colored noise**Author(s):**Fredkin, Donald R.; Rice, John A.; **Date issued:**Jun 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3q5n (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3q66 (PostScript) **Abstract:**Hidden Markov models have been used in the study of single-channel recordings of ion channel currents for restoration of idealized
signals from noisy recordings and for estimation of kinetic parameters. A key to their effectiveness from a computational
point of view is that the number of operations to evaluate the likelihood, posterior probabilities, and the most likely state
sequence are proportional to the product of the square of the dimension of the state space and the length of the series. However,
when the state space is quite large, computations can become infeasible. This can happen when the record has been low pass
filtered and when the noise is colored. In this paper we present an approximate method that can provide very substantial
reductions in computational cost at the expense of only a very small error. We describe the method and illustrate through
examples the gains that can be made in evaluating the likelihood.**Keyword note:**Fredkin__Donald_R Rice__John_Andrew**Report ID:**485**Relevance:**100

**Title:**Planning for the census in the year 2000: an update**Author(s):**Eaton, Morris L.; Freedman, David A.; Klein, Stephen P.; Olshen, Richard A.; Wachter, Kenneth W.; Ylvisaker, Donald; **Date issued:**Jun 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3q20 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3q3j (PostScript) **Abstract:**This paper is a discussion of Census 2000, focusing on planned use of sampling techniques for non-response followup and adjustment.**Keyword note:**Eaton__Morris_L Freedman__David Klein__Stephen_P Olshen__Richard_A Wachter__Kenneth Ylvisaker__Donald**Report ID:**484**Relevance:**100

**Title:**Exploring Quasi Monte Carlo for Marginal Density Approximation**Author(s):**Ostland, Michael; Yu, Bin; **Date issued:**May 1997**Keyword note:**Ostland__Michael_Anthony Yu__Bin**Report ID:**483**Relevance:**100

**Title:**Enumerations of trees and forests related to branching processes and random walks**Author(s):**Pitman, Jim; **Date issued:**May 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3p6p (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3p77 (PostScript) **Abstract:**In a Galton-Watson branching process with offspring distribution $(p_0, p_1, \ldots )$ started with $k$ individuals, the
distribution of the total progeny is identical to the distribution of the first passage time to $-k$ for a random walk started
at 0 which takes steps of size $j$ with probability $p_(j+1)$ for $j \ge -1$. The formula for this distribution is a probabilistic
expression of the Lagrange inversion formula for the coefficients in the power series expansion of $f(z)^k$ in terms of those
of $g(z)$ for $f(z)$ defined implicitly by $f(z) = z g(f(z))$. The Lagrange inversion formula is the analytic counterpart
of various enumerations of trees and forests which generalize Cayley's formula $k n^(n-k-1)$ for the number of rooted forests
labeled by a set of size $n$ whose set of roots is a particular subset of size $k$. These known results are derived by elementary
combinatorial methods without appeal to the Lagrange formula, which is then obtained as a byproduct. This approach unifies
and extends a number of known identities involving the distributions of various kinds of random trees and random forests.**Pub info:**In Microsurveys in Discrete Probability edited by D. Aldous and J. Propp. DIMACS Ser. Discrete Math. Theoret. Comput. Sci..**Keyword note:**Pitman__Jim**Report ID:**482**Relevance:**100

**Title:**Tree-valued Markov chains derived from Galton-Watson processes.**Author(s):**Aldous, David; Pitman, Jim; **Date issued:**Feb 1997

http://nma.berkeley.edu/ark:/28722/bk0000n3p31 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3p4k (PostScript) **Abstract:**Let $G$ be a Galton-Watson tree, i.e. the family tree of a Galton-Watson branching process. For $0 \leq u \leq 1$ let $G_u$
be the subtree of $G$ obtained by retaining each edge with probability $u$ and deleting other edges. We study the tree-valued
Markov process $(G_u, 0 \leq u \leq 1)$ and an analogous process $(G^*_u, 0 \leq u \leq 1)$ in which $G^*_1$ is a critical
or subcritical Galton-Watson tree conditioned to be infinite. Results simplify and are further developed in the special case
of Poisson$(\mu)$ offspring distribution.**Pub info:**Ann. Inst. Henri. Poincar\'e 34, 1998, 637-686**Keyword note:**Aldous__David_J Pitman__Jim**Report ID:**481**Relevance:**100