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作者：Samorodnitsky, Gennady; Wang, Yizao
作者单位：Cornell University; University System of Ohio; University of Cincinnati
摘要：We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one regime, our results exhibit limits that are not among the classical extreme value distributions. Restricted to the one-dimensional case, the distributions we obtain interpolate, in the appropriate parameter range, the alpha-Frechet distribution and the skew...
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作者：Etheridge, Alison M.; Kurtz, Thomas G.
作者单位：University of Oxford; University of Wisconsin System; University of Wisconsin Madison
摘要：Representations of population models in terms of countable systems of particles are constructed, in which each particle has a type, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, lambda], whereas in the infinite intensity limit lambda -> infinity, at each time t, the joint distribution of types and levels is conditionally Poisson, with mean measure Xi(t) x l where l denotes Lebesgue measure and Xi(t) is a ...
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作者：Gamarnik, David; Ramanan, Kavita
作者单位：Massachusetts Institute of Technology (MIT); Brown University
摘要：We formulate a continuous version of the well-known discrete hardcore (or independent set) model on a locally finite graph, parameterized by the so-called activity parameter lambda > 0. In this version the state or spin value x(u) of any node u of the graph lies in the interval [0, 1], the hardcore con- straint x(u) + x(v) <= 1 is satisfied for every edge (u, v) of the graph, and the space of feasible configurations is given by a convex polytope. When the graph is a regular tree, we show that ...
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作者：Maples, Kenneth; Najnudel, Joseph; Nikeghbali, Ashkan
作者单位：University of Zurich; University System of Ohio; University of Cincinnati
摘要：It is known that a unitary matrix can be decomposed into a product of complex reflections, one for each dimension, and that these reflections are independent and uniformly distributed on the space where they live if the initial matrix is Haar-distributed. If we take an infinite sequence of such reflections, and consider their successive products, then we get an infinite sequence of unitary matrices of increasing dimension, all of them following the circular unitary ensemble. In this coupling, ...
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作者：Basak, Anirban; Rudelson, Mark
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Weizmann Institute of Science; University of Michigan System; University of Michigan
摘要：For a class of sparse random matrices of the form A(n) = (xi(i, j)delta(i, j))(i)(n), j=1 where {xi(i, j)} are i.i.d. centered sub-Gaussian random variables of unit variance, and {delta(i, j)} are i.i.d. Bernoulli random variables taking value 1 with probability p(n), we prove that the empirical spectral distribution of An/root np(n) converges weakly to the circular law, in probability, for all p(n) such that p(n) = omega (log(2) n/n). Additionally if p(n) satisfies the inequality np(n) > exp(...
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作者：Cortines, Aser; Hartung, Lisa; Louidor, Oren
作者单位：University of Zurich; New York University; Technion Israel Institute of Technology
摘要：We study the structure of extreme level sets of a standard one-dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height of the local maxima ...
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作者：Dolgopyat, Dmitry; Goldsheid, Ilya
作者单位：University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of London; Queen Mary University London
摘要：Environment viewed from the particle is a powerful method of analyzing random walks (RW) in random environment (RE). It is well known that in this setting the environment process is a Markov chain on the set of environments. We study the fundamental question of existence of the density of the invariant measure of this Markov chain with respect to the measure on the set of environments for RW on a strip. We first describe all positive subexponentially growing solutions of the corresponding inva...
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作者：Auffinger, Antonio; Jagannath, Aukosh
作者单位：Northwestern University; Harvard University
摘要：We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, <.>(N), into a mixture of conditional laws, <.>(alpha,N). We show that the TAP equations hold for the spin at any site with respect to <.>(alpha,N) simultaneously for all alpha. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.
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作者：Breuillard, Emmanuel; Varju, Peter P.
作者单位：University of Cambridge
摘要：The Bernoulli convolution with parameter lambda is an element of (0, 1) is the probability measure mu(lambda) that is the law of the random variable Sigma(n >= 0) +/-lambda(n), where the signs are independent unbiased coin tosses. We prove that each parameter lambda is an element of (1/2, 1) with dim mu(lambda) < 1 can be approximated by algebraic parameters eta is an element of (1/2, 1) within an error of order exp(- deg(eta)(A)) such that dim mu(eta) < 1, for any number A. As a corollary, we...
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作者：Fathi, Max
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
摘要：We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Ampere equation. As a consequence, we show how regularity bounds in certain weighted Sobolev spaces on these maps control the rate of convergence in the classical central limit theorem, and derive new rates in Kantorovitch-Wasserstein distance in the log-concave situation, with explicit polynomial dependence on the dimension.
