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作者：Caputo, Pietro; Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan; Toninelli, Fabio Lucio
作者单位：Roma Tre University; Microsoft; University of California System; University of California Berkeley; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We study the Glauber dynamics for the (2 + 1)D Solid-On-Solid model above a hard wall and below a far away ceiling, on an L x L box of Z(2) with zero boundary conditions, at large inverse-temperature P. It was shown by Bricmont, El Mellouki and Frohlich [J. Stat. Phys. 42 (1986) 743-798] that the floor constraint induces an entropic repulsion effect which lifts the surface to an average height H um log L. As an essential step in understanding the effect of entropic repulsion on the Glauber dyn...
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作者：Ding, Jian
作者单位：Stanford University; University of Chicago
摘要：In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, assuming that the maximal hitting time is significantly smaller than the cover time. Previously, this was only proved for regular trees and the 2D lattice. Furthermore, for general trees, we derive exponential concentration for the cover time,...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：We consider the initial boundary value problem ut = mu u(x) + 1/2u(xx) (t > 0, x >= 0) u(0, x) = f(x) (x >= 0), u(t)(t, 0) = vu(x) (t, 0) (t > 0) of Stroock and Williams [Comm. Pure Appl. Math. 58 (2005) 1116-1148] where, mu, v is an element of R and the boundary condition is not of Feller's type when v <0. We show that when f belongs to C-b(1) with f (infinity) = 0 then the following probabilistic representation of the solution is valid: u(t, x) = Ex[f'(Xt)integral(0) (lt0(x)) (e-2(v - mu)s) ...
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作者：Eisenbaum, Nathalie
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We solve a conjecture raised by Evans in 1991 on the characterization of the positively correlated squared Gaussian vectors. We extend this characterization from squared Gaussian vectors to permanental vectors. As side results, we obtain several equivalent formulations of the property of infinite divisibility for squared Gaussian processes.
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作者：Lalley, Steven P.; Perkins, Edwin A.; Zheng, Xinghua
作者单位：University of Chicago; University of British Columbia; Hong Kong University of Science & Technology
摘要：We consider measure-valued processes X = (X-t) that solve the following martingale problem: for a given initial measure X-0, and for all smooth, compactly supported test functions phi, X-t(phi) = X-0(phi) + 1/2 integral(t)(0)Xs(Delta phi) ds + 1/2 integral(t)(0) Xs (phi) ds -integral(t)(0)Xs(L-s phi) ds + M-t(phi) Here Ls(x) is the local time density process associated with X, and Mt (co) is a martingale with quadratic variation [M-t(phi)](t) =integral(t)(0)Xs(phi(2)) ds. Such processes arise ...
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作者：Mackey, Lester; Jordan, Michael I.; Chen, Richard Y.; Farrell, Brendan; Tropp, Joel A.
作者单位：Stanford University; University of California System; University of California Berkeley; University of California System; University of California Berkeley; California Institute of Technology
摘要：This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers b...
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作者：Nourdin, Ivan; Rosinski, Jan
作者单位：Universite de Lorraine; University of Tennessee System; University of Tennessee Knoxville
摘要：We characterize the asymptotic independence between blocks consisting of multiple Wiener-Ito integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension and other related results on the multivariate convergence of multiple Wiener-Ito integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long-range dependent st...
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作者：Cerrai, Sandra; Da Prato, Giuseppe
作者单位：University System of Maryland; University of Maryland College Park; Scuola Normale Superiore di Pisa
摘要：We consider the Kolmogorov operator associated with a reaction diffusion equation having polynomially growing reaction coefficient and perturbed by a noise of multiplicative type, in the Banach space E of continuous functions. By analyzing the smoothing properties of the associated transition semigroup, we prove a modification of the classical identite du carre des champs that applies to the present non-Hilbertian setting. As an application of this identity, we construct the Sobolev space W-1,...
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作者：Handa, Kenji
作者单位：Saga University
摘要：We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.
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作者：Goetze, Friedrich; Zaitsev, Andrei Yu
作者单位：University of Bielefeld; Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：Let X, X-1, X-2,... be i.i.d. R-d-valued real random vectors. Assume that EX = 0, cov X = C, E vertical bar vertical bar X vertical bar vertical bar(2) = sigma(2) and that X is not concentrated in a proper subspace of R-d Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms Q[S-N] of the normalized sums S-N = N-(1/2) (X-1 +...+ X-N) and show that, without any additional conditions, Delta(N) =(def...
