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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...
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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.
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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...
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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.
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作者：Dembo, Amir; Tsai, Li-Cheng
作者单位：Stanford University; Stanford University; Columbia University
摘要：We study the fluctuation of the Atlas model, where a unit drift is assigned to the lowest ranked particle among a semi-infinite (Z(+)-indexed) system of otherwise independent Brownian particles, initiated according to a Poisson point process on R+. In this context, we show that the joint law of ranked particles, after being centered and scaled by t(-1/4), converges as t -> infinity to the Gaussian field corresponding to the solution of the Additive Stochastic Heat Equation (ASHE) on R+ with th...
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作者：Hairer, Martin; Shen, Hao
作者单位：University of Warwick; University of Warwick; Columbia University
摘要：We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the Hopf-Cole solution to the KPZ equation driven by space-time Gaussian white noise. While the limiting process depends only on the integrated variance o...
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作者：Comets, Francis; Popov, Serguei
作者单位：Universite Paris Cite; Universidade Estadual de Campinas; Universite Paris Cite; Universidade Estadual de Campinas
摘要：For the model of two-dimensional random interlacements in the critical regime (i.e., alpha = 1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [Commun. Math. Phys. 343 (2016) 129-164]. Also, we prove that the entrance measure of simple random walk on annular domains has certain regularity properties; this result is useful when dealing with soft local times for excursion processes.
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作者：Auffinger, Antonio; Chen, Wei-Kuo
作者单位：Northwestern University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
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作者：Basse-O'Connor, Andreas; Lachieze-Rey, Raphael; Podolskij, Mark
作者单位：Aarhus University; Universite Paris Cite
摘要：In this paper, we present some new limit theorems for power variation of kth order increments of stationary increments Levy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while the time span remains fixed, the asymptotic theory gives novel results, which (partially) have no counterpart in the theory of discrete moving averages. More specifically, we show that the first-order limit theory and the mode of convergence strongly depend on th...
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作者：Alsmeyer, Gerold; Kabluchko, Zakhar; Marynych, Alexander
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：Motivated by the open problem of finding the asymptotic distributional behavior of the number of collisions in a Poisson-Dirichlet coalescent, the following version of a stochastic leader-election algorithm is studied. Consider an infinite family of persons, labeled by 1, 2, 3,..., who generate i.i.d. random numbers from an arbitrary continuous distribution. Those persons who have generated a record value, that is, a value larger than the values of all previous persons, stay in the game, all o...
