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作者：Mueller, Carl; Mytnik, Leonid; Perkins, Edwin
作者单位：University of Rochester; Technion Israel Institute of Technology; University of British Columbia
摘要：Motivated by Girsanov's nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) partial derivative u/partial derivative t = Delta/2 u(t, x) + vertical bar u(t, x)vertical bar(gamma) W(t, x), u(0, x) = 0 Here W is a space time white noise on R x R. More precisely, we show the above stochastic PDE has a nonzero solution for 0 < y < 3/4. Since u(t, x) = 0 solves the equation, it follows that solutions are neither unique in law nor ...
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作者：Garet, Olivier; Marchand, Regine
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The asymptotic shape theorem for the contact process in random environment gives the existence of a norm mu on R-d such that the hitting time t(x) is asymptotically equivalent to mu(x) when the contact process survives. We provide here exponential upper bounds for the probability of the event {t(x)/mu(x) is not an element of[1 - epsilon, 1 + epsilon]); these bounds are optimal for independent random environment. As a special case, this gives the large deviation inequality for the contact proce...
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作者：Alberts, Tom; Khanin, Konstantin; Quastel, Jeremy
作者单位：California Institute of Technology; University of Toronto
摘要：We introduce a new disorder regime for directed polymers in dimension 1 + 1 that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter beta to zero as the polymer length n tends to infinity. The natural choice of scaling is beta(n) :=beta n(-1/4). We show that the polymer measure under this scaling has previously unseen behavior. While the fluctuation exponents of the polymer endpoint and the ...
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作者：Denis, Laurent; Matoussi, Anis; Zhang, Jing
作者单位：Universite Paris Saclay; Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying the minimal Skohorod condition.
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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...
