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作者：Kleptsyn, Victor; Kurtzmann, Aline
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we construct a counterexample to a question by Cantelli, asking whether there exists a nonconstant positive measurable function phi such that for i.i.d. r.v. X, Y of law N(0, 1), the r.v. X + phi(X) . Y is also Gaussian. This construction is made by finding an unusual solution to the Skorokhod embedding problem (showing that the corresponding Brownian transport, contrary to the Root barrier, is not unique). To find it, we establish some sufficient conditions for the continuity o...
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作者：Kharroubi, Idris; Huyen Pham
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris
摘要：We aim to provide a Feynman-Kac type representation for Hamilton Jacobi-Bellman equation, in terms of forward backward stochastic differential equation (FBSDE) with a simulatable forward process. For this purpose, we introduce a class of BSDE where the jumps component of the solution is subject to a partial nonpositive constraint. Existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions. We then show how minimal solution to this BSDE cl...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppaelaeinen, Timo; Yilmaz, Atilla
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Bogazici University
摘要：We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit of quenched polymer measures. We prove this limit for the exactly solvable log-gamma polymer, as a consequence of almost sure limits of ratios of partition functions. These limits of ratios give the Busemann functions of the log-gamma polymer, and furnish cen...
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作者：Berestycki, Nathanael; Garban, Christophe; Sen, Arnab
作者单位：University of Cambridge; 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; University of Minnesota System; University of Minnesota Twin Cities
摘要：The coalescing Brownian flow on R is a process which was introduced by Arratia [Coalescing Brownian motions on the line (1979) Univ. Wisconsin, Madison] and Toth and Werner [Probab. Theory Related Fields 111 (1998) 375-452], and which formally corresponds to starting coalescing Brownian motions from every space-time point. We provide a new state space and topology for this process and obtain an invariance principle for coalescing random walks. This result holds under a finite variance assumpti...
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作者：Khoshnevisan, Davar; Kim, Kunwoo
作者单位：Utah System of Higher Education; University of Utah
摘要：Consider the stochastic heat equation partial derivative(t)u = Lu + lambda sigma (u)xi, where L denotes the generator of a Levy process on a locally compact Hausdorff Abelian group G, sigma : R -> R is Lipschitz continuous, lambda >> 1 is a large parameter, and xi denotes space time white noise on R+ x G. The main result of this paper contains a near-dichotomy for the (expected squared) energy E(parallel to u(t)parallel to(2)(L2(G))) of the solution. Roughly speaking, that dichotomy says that,...
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作者：Mathieu, P.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We show that the asymptotic entropy of a random walk on a nonelementary hyperbolic group, with symmetric and bounded increments, is differentiable and we identify its derivative as a correlation. We also prove similar results for the rate of escape.
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作者：Kortchemski, Igor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We study large random dissections of polygons. We consider random dissections of a regular polygon with n sides, which are chosen according to Boltzmann weights in the domain of attraction of a stable law of index theta is an element of (1, 2]. As n goes to infinity, we prove that these random dissections converge in distribution toward a random compact set, called the random stable lamination. If theta = 2, we recover Aldous' Brownian triangulation. However, if theta is an element of (1, 2), ...
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作者：Rhodes, Remi; Sohier, Julien; Vargas, Vincent
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Eindhoven University of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous e...
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作者：Glatt-Holtz, Nathan E.; Vicol, Vlad C.
作者单位：Indiana University System; Indiana University Bloomington; University of Chicago
摘要：We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the three-dimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occur...
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作者：Johnson, Tobias; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：Consider the sum of d many i.i.d. random permutation matrices on n labels along with their transposes. The resulting matrix is the adjacency matrix of a random regular (multi)-graph of degree 2d on n vertices. It is known that the distribution of smooth linear eigenvalue statistics of this matrix is given asymptotically by sums of Poisson random variables. This is in contrast with Gaussian fluctuation of similar quantities in the case of Wigner matrices. It is also known that for Wigner matric...
