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作者：Kious, Daniel
摘要：In this paper, we work on a class of self-interacting nearest neighbor random walks, introduced in [Probab. Theory Related Fields 154 (2012) 149-163], for which there is competition between repulsion of neighboring edges and attraction of next-to-neighboring edges. Erschler, Toth and Werner proved in [Probab. Theory Related Fields 154 (2012) 149-163] that, for any L >= 1, if the parameter alpha belongs to a certain interval (alpha(L+1), alpha(L)), then such random walks localize on L + 2 sites...
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作者：Rossignol, Raphael
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem f...
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作者：Ziliotto, Bruno
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole
摘要：Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guarantee the asymptotic value. We disprove these two long-standing conjectures by providing an example of ...
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作者：Li, Xue-Mei
作者单位：University of Warwick
摘要：We study random perturbation to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm 1. We prove that the projections of the solutions to the perturbed equations, converge, after suitable resealing, to a Brownian motion scaled by 8/n(n-1) where n is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal ...
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作者：Rudelson, Mark; Samorodnitsky, Alex; Zeitouni, Ofer
作者单位：University of Michigan System; University of Michigan; Hebrew University of Jerusalem; Weizmann Institute of Science; New York University
摘要：We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok's estimator gives a polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect ma...
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作者：Da Prato, G.; Flandoli, F.; Rockner, M.; Veretennikov, A. Yu.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Bielefeld; University of Leeds; HSE University (National Research University Higher School of Economics); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the sub-differential of a convex function and a bounded part. This generalizes a classical result by one of the authors to infinite dimensions. Our results also generalize and improve recent results by N. Champagnat and P. E. Jabin, proved in finite dimensions, in the case where their diffusion matrix is constant and nond...
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作者：Ren, Jiagang; Wu, Jing
作者单位：Sun Yat Sen University
摘要：In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Sole's idea, we characterize in Holder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of ...
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作者：Estrade, Anne; Leon, Jose R.
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Central Venezuela
摘要：We study the Euler characteristic of an excursion set of a stationary isotropic Gaussian random field X : Omega x R-d -> R. Let us fix a level u is an element of R and let us consider the excursion set above u, A(T, u) = {t is an element of T : X(t) >= u} where T is a bounded cube subset of R-d. The aim of this paper is to establish a central limit theorem for the Euler characteristic of A(T,u) as T grows to R-d, as conjectured by R. Adler more than ten years ago [Ann. Appl. Probab. 10 (2000) ...
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作者：Mastrolia, Thibaut; Possamai, Dylan; Reveillac, Anthony
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
摘要：In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution (Y, Z) to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin-Viens formula, we provide estimates on these densities.
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作者：Debicki, Krzysztof; Hashorva, Enkelejd; Ji, Lanpeng
作者单位：University of Wroclaw
摘要：This contribution establishes exact tail asymptotics of sup((s,t)) is an element of E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E subset of R-2, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applications of our result include the derivation of the exact tail asymptotics of ...
