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作者：Gassiat, Paul; Gess, Benjamin; Lions, Pierre-Louis; Souganidis, Panagiotis E.
作者单位：Universite PSL; Universite Paris-Dauphine; Max Planck Society; University of Bielefeld; Universite PSL; College de France; University of Chicago
摘要：We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of dependence is bounded by a multiple of the length of the skeleton of the path, that is a piecewise linear path obtained by connecting the successive extrema of the original one. When the driving path is a Brownian motion, we prove that its skeleton has almost sur...
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作者：Bertoin, Jean
作者单位：University of Zurich
摘要：A reinforcement algorithm introduced by Simon (Biometrika 42(3/4):425-440, 1955) produces a sequence of uniform random variables with long range memory as follows. At each step, with a fixed probability p is an element of (0, 1), (U) over cap (n+1) is sampled uniformly from (U) over cap (1), ... , (U) over cap (n), and with complementary probability 1 - p, (U) over cap (n+1) is a new independent uniform variable. The Glivenko-Cantelli theorem remains valid for the reinforced empirical measure,...
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作者：Eldan, Ronen; Mikulincer, Dan
作者单位：Weizmann Institute of Science
摘要：We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation distance. In particular, we give the first stability estimate for general log-concave random vectors in the following form: for log-concave random vectors X, Y. Rd, the deficit in the Shannon-Stam inequality is bounded from below by the expression C (D(X||G) + D(Y ||G)), where D(. ||G) denotes the relative entropy with r...
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作者：Bordenave, Charles; Lugosi, Gabor; Zhivotovskiy, Nikita
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Pompeu Fabra University; ICREA; Alphabet Inc.; Google Incorporated
摘要：We investigate the noise sensitivity of the top eigenvector of a Wigner matrix in the following sense. Let v be the top eigenvector of an NxN Wigner matrix. Suppose that k randomly chosen entries of the matrix are resampled, resulting in another realization of the Wigner matrix with top eigenvector v[k]. We prove that, with high probability, when kMUCH LESS-THANN5/3-o(1), then v and v[k] are almost collinear and when k >> N5/3, then v[k] is almost orthogonal to v.
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作者：Gnedin, Alexander; Iksanov, Alexander
作者单位：University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity. In the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in Ewens' and mor...
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作者：Lambert, Amaury; Schertzer, Emmanuel
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Biology (INSB); Universite PSL; College de France; Ecole Normale Superieure (ENS); Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：The nested Kingman coalescent describes the dynamics of particles (called genes) contained in larger components (called species), where pairs of species coalesce at constant rate and pairs of genes coalesce at constant rate provided they lie within the same species. We prove that starting from rn species, the empirical distribution of species masses (numbers of genes/n) at time t/n converges as n -> infinity to a solution of the deterministic coagulation-transport equation partial derivative(t...
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作者：Bonis, Thomas
作者单位：Universite Paris Saclay
摘要：We use Stein's method to bound the Wasserstein distance of order 2 between a measure nu and the Gaussian measure using a stochastic process (X-t)(t >= 0) such that X-t is drawn from nu for any t > 0. If the stochastic process (X-t)(t >= 0) satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds onWasserstein distances of any order p >= 1. Using our results, we provide convergence rates for the multi-dimensional central limit theorem in terms of Wasserst...
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作者：Diaz, Mario; Mingo, James A.; Belinschi, Serban T.
作者单位：Queens University - Canada; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper we study the global fluctuations of block Gaussian matrices within the framework of second-order free probability theory. In order to compute the second-order Cauchy transform of these matrices, we introduce a matricial second-order conditional expectation and compute the matricial second-order Cauchy transform of a certain type of non-commutative random variables. As a by-product, using the linearization technique, we obtain the second-order Cauchy transform of non-commutative r...
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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very large class of graphs, including every transitive graph of at least quintic volume growth and every bounded degree nonamenable graph. Several of our results are new even in the case of Z(d), d >= 5. In particular, we prove that every tree in the forest has spectral dimension 4/3 and walk dimension 3 almost surely, and that the critical exponents governing the intrinsic diameter and volume of the past of a v...
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作者：van der Hofstad, Remco; Hulshof, Tim; Nagel, Jan
作者单位：Eindhoven University of Technology; Dortmund University of Technology
摘要：Let T be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean mu > 1, conditioned to survive. Let phi T be a random embedding of T into Z(d) according to a simple random walk step distribution. Let T-p be percolation on T with parameter p, and let p(c) = mu(-1) be the critical percolation parameter. We consider a random walk (X-n)(n >= 1) on T-p and investigate the behavior of the embedded process phi T-p (X-n) as n -> infinity and simultaneously, T-p becomes ...
