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作者：Gnedin, Alexander V.; Yakubovich, Yuri
作者单位：Utrecht University
摘要：A class of random discrete distributions P is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such P a power growth of the number of blocks is typical. Some known and some new partition structures appear when P is induced by a Dirichlet splitting.
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作者：Luczak, Malwina J.; McDiarmid, Colin
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：There are n queues, each with a single server. Customers arrive in a Poisson process at rate lambda n, where 0 < lambda < 1. Upon arrival each customer selects d >= 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with proba...
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作者：Bryc, W; Dembo, A; Jiang, TF
作者单位：University System of Ohio; University of Cincinnati; Stanford University; Stanford University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study the limiting spectral measure of large symmetric random matrices of linear algebraic structure. For Hankel and Toeplitz matrices generated by i.i.d. random variables {X-k} of unit variance, and for symmetric Markov matrices generated by i.i.d. random variables {X-ij} (j > i) of zero mean and unit variance, scaling the eigen-values by root n we prove the almost sure, weak convergence of the spectral measures to universal, nonrandom, symmetric distributions gamma(H), gamma(M) and gamma(...
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作者：Marckert, Jean-Francois; Mokkadem, Abdelkader
作者单位：Universite Paris Saclay
摘要：Consider q(n) a random pointed quadrangulation chosen equally likely among the pointed quadrangulations with n faces. In this paper we show that, when n goes to +infinity, qn suitably normalized converges weakly in a certain sense to a random limit object, which is continuous and compact, and that we name the Brownian map. The same result is shown for a model of rooted quadrangulations and for some models of rooted quadrangulations with random edge lengths. A metric space of rooted (resp. poin...
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作者：Goldstein, Larry; Xia, Aihua
作者单位：University of Southern California; University of Melbourne
摘要：We introduce a new family of distributions to approximate P(W epsilon A) for A subset of {...-2, -1, 0,1, 2...} and W a sum of independent integer-valued random variables xi(1), xi(2), ..., xi(n) with finite second moments, where, with large probability, W is not concentrated on a lattice of span greater than 1. The well-known Berry-Esseen theorem states that, for Z a normal random variable with mean E(W) and variance Var(W), P(Z epsilon A) provides a good approximation to P(W epsilon A) for A...
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作者：Gine, Evarist; Koltchinskii, Vladimir
作者单位：University of Connecticut; University of New Mexico
摘要：Let F be a class of measurable functions on a measurable space (S, S) with values in [0, 1] and let [GRAPHICS] be the empirical measure based on an i.i.d. sample (X-1,..., X-n) from a probability distribution P on (S, S). We study the behavior of suprema of the following type: [GRAPHICS] where sigma(p)f >= Var(p)(1/2) f and phi is a continuous, strictly increasing function with phi(0) = 0. Using Talagrand's concentration inequality for empirical processes, we establish concentration inequaliti...
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作者：Ben Arous, Gerard; Voiculescu, Dan Virgil
作者单位：New York University; University of California System; University of California Berkeley
摘要：Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using free extremal convolutions on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a measure-space is constructed, which is related to the free Poisson point process.
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作者：Lyons, Russell; Peres, Yuval; Schramm, Oded
作者单位：Indiana University System; Indiana University Bloomington; University of California System; University of California Berkeley; Microsoft
摘要：Minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs. These limits can be taken with free or wired boundary conditions and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively. The WMSF is also the union of the trees that arise from invasion percolation started at all vertices. We show that on any Cayley graph where critical percolation has no infinite clusters, all the component trees in t...
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作者：Gravner, J; Griffeath, D
作者单位：University of California System; University of California Davis; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for asymptotic shapes arising from finite initial seeds. Such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases. In many cases, exact stability is observed. That is, for small perturbations, t...
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作者：Bally, Vlad
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We give lower bounds for the density p(T) (x, y) of the law of X-t, the solution of dX(t) = sigma(X-t)dB(t) +b(X-t)dt, X-0 = x, under the following local ellipticity hypothesis: there exists a deterministic differentiable curve x(t), 0 <= t <= T, such that x(0) = x, x(T) = y and sigma sigma* (x(t)) > 0, for all t is an element of [0, T]. The lower bound is expressed in terms of a distance related to the skeleton of the diffusion process. This distance appears when we optimize over all the curv...
