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作者：Peres, Yuval; Sousi, Perla; Steif, Jeffrey E.
作者单位：Microsoft; University of Cambridge; Chalmers University of Technology; University of Gothenburg
摘要：We consider dynamical percolation on the d-dimensional discrete torus Zndof side length n, where each edge refreshes its status at rate mu=mu n <= 1/2 to be open with probability p. We study random walk on the torus, where the walker moves at rate 1 / (2d) along each open edge. In earlier work of two of the authors with A. Stauffer, it was shown that in the subcritical case p1/2. When theta(p)>0, we prove a version of this conjecture for an alternative notion of mixing time involving randomise...
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作者：Pal, Soumik; Wong, Ting-Kam Leonard
作者单位：University of Washington; University of Washington Seattle; University of Toronto
摘要：We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a particle system of Dirichlet processes transporting one probability measure on the unit simplex to another by coordinatewise multiplication and normalizing. The structure of our Lagrangian and the appearance of the Dirichlet process relate our problem closely...
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作者：Duerinckx, Mitia; Gloria, Antoine; Otto, Felix
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite Libre de Bruxelles; Max Planck Society
摘要：We consider a linear elliptic system in divergence form with random coefficients and study the random fluctuations of large-scale averages of the field and the flux of the solution operator. In the context of the random conductance model, we developed in a previous work a theory of fluctuations based on the notion of homogenization commutator: we proved that the two-scale expansion of this special quantity is accurate at leading order in the fluctuation scaling when averaged on large scales (a...
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作者：Belius, David; Rosen, Jay; Zeitouni, Ofer
作者单位：University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
摘要：Let CE,S2 denote the cover time of the two dimensional sphere by a Wiener sausage of radius E. We prove that CE,S2AS2 pi logE-1-loglogE-1is tight, where AS2=4 pi denotes the Riemannian area of S2.
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the bottom of the spectrum of the Anderson Hamiltonian H-L := -partial derivative(2)(x) + xi on [0, L] driven by a white noise xi and endowed with either Dirichlet or Neumann boundary conditions. We show that, as L -> infinity, the point process of the (appropriately shifted and rescaled) eigenvalues converges to a Poisson point process on R with intensity e(x)dx, and that the (appropriately rescaled) eigenfunctions converge to Dirac masses located at independent and uniformly distrib...
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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...
