-
作者：Gantert, Nina; Kim, Steven Soojin; Ramanan, Kavita
作者单位：Technical University of Munich; Brown University
摘要：Let p is an element of[ 1,infinity]. Consider the projection of a uniform random vector from a suitably normalized l(p) ball in R-n onto an independent random vector from the unit sphere. We show that sequences of such random projections, when suitably normalized, satisfy a large deviation principle (LDP) as the dimension n goes to infinity, which can be viewed as an annealed LDP. We also establish a quenched LDP (conditioned on a fixed sequence of projection directions) and show that for p is...
-
作者：Hu, Yaozhong; Huang, Jingyu; Le, Khoa; Nualart, David; Tindel, Samy
作者单位：University of Kansas; Purdue University System; Purdue University
摘要：This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (1/4, 1/2) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient sigma(u) is differentiable with a Lipschitz derivative and sigma(0) = 0.
-
作者：Cuny, Christophe
作者单位：Universite Paris Saclay
摘要：We prove that, for (adapted) stationary processes, the so-called Maxwell-Woodroofe condition is sufficient for the law of the iterated logarithm and that it is optimal in some sense. That result actually holds in the context of Banach valued stationary processes, including the case of L-P-valued random variables, with 1 <= p < infinity. In this setting, we also prove the weak invariance principle, hence generalizing a result of Peligrad and Utev [Ann. Probab. 33 (2005) 798-815]. The proofs mak...
-
作者：Sapozhnikov, Artem
作者单位：Leipzig University
摘要：For a general class of percolation models with long-range correlations on Zd, d >= 2, introduced in [J. Math. Phys. 55 (2014) 083307], we establish regularity conditions of Barlow [Ann. Probab. 32 (2004) 3024-3084] that mesoscopic subballs of all large enough balls in the unique infinite percolation cluster have regular volume growth and satisfy a weak Poincare inequality. As immediate corollaries, we deduce quenched heat kernel bounds, parabolic Harnack inequality, and finiteness of the dimen...
-
作者：Curien, Nicolas; Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius n centered at the root, we prove that, although the size of the boundary is of order n, most of the harmonic measure is supported on a boundary set of size approximately equal to n(beta), where beta approximate to 0.78 is a universal constant. To derive such results, we interpret harmonic measure as the exit distribution of the ball by simple random walk on the tree, and we first deal wit...
-
作者：Bauerschmidt, Roland; Huang, Jiaoyang; Knowles, Antti; Yau, Horng-Tzer
作者单位：University of Cambridge; Harvard University; University of Geneva
摘要：We consider the uniform random d-regular graph on N vertices, with d is an element of [N-alpha, N2/3-alpha] for arbitrary alpha > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.
-
作者：Campos, David; Ramirez, Alejandro F.
作者单位：Universidad Costa Rica; Pontificia Universidad Catolica de Chile
摘要：We consider a random walk in random environment in the low disorder regime on Z(d), that is, the probability that the random walk jumps from a site x to a nearest neighboring site x + e is given by p(e) + epsilon xi(x, e), where p(e) is deterministic, {{xi(x, e) : vertical bar e vertical bar(1) = 1} : x is an element of Z(d)} are i.i.d. and epsilon > 0 is a parameter, which is eventually chosen small enough. We establish an asymptotic expansion in epsilon for the invariant measure of the envir...
-
作者：Eisenbaum, Nathalie; Maunoury, Franck
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Sorbonne Universite
摘要：Existence conditions of permanental distributions are deeply connected to existence conditions of multivariate negative binomial distributions. The aim of this paper is twofold. It answers several questions generated by recent works on this subject, but it also goes back to the roots of this field and fixes existing gaps in older papers concerning conditions of infinite divisibility for these distributions.
-
作者：Cheridito, Patrick; Nam, Kihun
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Rutgers University System; Rutgers University New Brunswick
摘要：In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be translated into a fixed-point problem in a space of random vectors. This makes it possible to employ general fixed-point arguments to establish the existence of a solution. For instance, Banach's contraction mapping theorem can be used to derive general existence...
-
作者：Angel, Omer; Kolesnik, Brett; Miermont, Gregory
作者单位：University of British Columbia; Ecole Normale Superieure de Lyon (ENS de LYON); Institut Universitaire de France
摘要：The Brownian map is a random geodesic metric space arising as the scaling limit of random planar maps. We strengthen the so-called confluence of geodesics phenomenon observed at the root of the map, and with this, reveal several properties of its rich geodesic structure. Our main result is the continuity of the cut locus at typical points. A small shift from such a point results in a small, local modification to the cut locus. Moreover, the cut locus is uniformly stable, in the sense that any ...
