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作者：Marcus, Michael B.; Rosen, Jay
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：An alpha-permanental process {X-t, t is an element of T} is a stochastic process determined by a kernel K = {K (s, t), s, t is an element of T}, with the property that for all t(1),..., t(n) is an element of T, vertical bar I + K(t(1),..., t(n)) S vertical bar(-alpha) is the Laplace transform of (X-t1,...,X-tn), where K (t(1),...,t(n)) denotes the matrix {K(t(i), t(j))}(i,j)(n) = 1 and S is the diagonal matrix with entries s(1),...,s(n). (X-t1,..., X-tn) s called a permanental vector. Under th...
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作者：Barchiesi, Marco; Brancolini, Alessio; Julin, Vesa
作者单位：University of Naples Federico II; University of Munster; University of Jyvaskyla
摘要：We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half- space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half- space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate...
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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...
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作者：Dalang, Robert C.; Mueller, Carl; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Michigan State University
摘要：We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space-time white noise, or colored noise in spatial dimensions k >= 1. Our approach builds on a delicate covering argument developed by M. Talagrand [Ann. Probab. 23 (1995) 767-775; Probab. The...
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作者：Paquette, Elliot; Zeitouni, Ofer
作者单位：University System of Ohio; Ohio State University; New York University; Weizmann Institute of Science
摘要：Let lambda((N)) be the largest eigenvalue of the N x N GUE matrix which is the Nth element of the GUE minor process, rescaled to converge to the standard Tracy-Widom distribution. We consider the sequence {lambda((N))}(N >= 1) and prove a law of fractional logarithm for the lim sup: lim sup(N ->infinity) lambda((N)) / (logN)(2/3) = (1/4)(2/3) almost surely. For the lim inf, we prove the weaker result that there are constants c(1), c(2) > 0 so that -c(1) <= lim inf(N ->infinity) lambda((N)) / (...
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作者：Caravenna, Francesco; Toninelli, Fabio Lucid; Torri, Niccolo
作者单位：University of Milano-Bicocca; 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; 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 consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent alpha is an element of (1/2, 1). This corresponds to a regime where disorder is known to be relevant, that is, to change the critical exponent of the localization transition and to induce a nontrivial shift of the critical point. We show that the free energy and critical curve have an explicit universal asymptotic behavior in the weak coupling regime, d...
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作者：Bally, Vlad; Caramellino, Lucia
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Rome Tor Vergata
摘要：Fournier and Printems [Bernoulli 16 (2010) 343-360] have recently established a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Holder continuous coefficients. This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus. By employing some Besov space techniques, Debussche and Romito [Probab. Theory Related Fields 158 (2014) 575-596] have substantially improved the result of Fo...
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作者：Dalang, Robert C.; Humeau, Thomas
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We identify a necessary and sufficient condition for a Levy white noise to be a tempered distribution. More precisely, we show that if the Levy measure associated with this noise has a positive absolute moment, then the Levy white noise almost surely takes values in the space of tempered distributions. If the Levy measure does not have a positive absolute moment of any order, then the event on which the Levy white noise is a tempered distribution has probability zero.
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作者：Ding, Jian; Roy, Rishideep; Zeitouni, Ofer
作者单位：University of Chicago; Indian Institute of Management (IIM System); Indian Institute of Management Bangalore; Weizmann Institute of Science; New York University
摘要：We show that the centered maximum of a sequence of logarithmically correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a randomly shifted Gumbel distribution, and characterize the random shift as the limit in distribution of a sequence of random variables, reminiscent of the derivative martingale in the theory of branching random walk and Gaussian chaos. We also dis...
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作者：Toninelli, Fabio Lucio
作者单位：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 introduce a class of (2 + 1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. Irreversible means that the interface has an average nonzero drift. Interface configurations correspond to height functions of dimer coverings of the infinite hexagonal or square lattice. The model can also be viewed as an interacting driven particle system and in the totally asymmetric case the dynamics corresponds to an infinite collection of mutua...
