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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：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 ...
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of N cards. We prove that around time N-2 logN/(2 pi(2)), the total variation distance to equilibrium of the deck distribution drops abruptly from 1 to 0, and that the separation distance has a similar behavior but with a transition occurring at time (N-2 logN)/pi(2). This solves a conjecture formulated by David Wilson. We present also similar results for the exclusion process on a segment of length ...
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作者：Duminil-Copin, Hugo; Glazman, Alexander; Hammond, Alan; Manolescu, Ioan
作者单位：University of Geneva; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; University of Oxford
摘要：We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z(d) for d >= 2. We show that the probability that a walk of length n ends at a point x tends to 0 as n tends to infinity, uniformly in x. Also, when x is fixed, with parallel to x parallel to = 1, this probability decreases faster than n(-1/4+epsilon) for any epsilon > 0. This provides a bound on the probability that a self-avoiding walk is a polygon.
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作者：Duminil-Copin, Hugo; van Enter, Aernout
作者单位：University of Geneva; University of Groningen
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作者：Ricard, Eric; Xu, Quanhua
作者单位：Universite de Caen Normandie; Wuhan University; Universite Marie et Louis Pasteur
摘要：Let M be a von Neumann algebra equipped with a faithful semifinite normal weight phi and N be a von Neumann subalgebra of M such that the restriction of phi to N is semifinite and such that N is invariant by the modular group of phi. Let epsilon be the weight preserving conditional expectation from M onto N. We prove the following inequality: parallel to x parallel to(2)(p) >= parallel to epsilon(x)parallel to(2)(p) + (p - 1)parallel to x - epsilon(x)parallel to(2)(p), x is an element of L-p(M...
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作者：Azmoodeh, Ehsan; Malicet, Dominique; Mijoule, Guillaume; Poly, Guillaume
作者单位：University of Luxembourg; Universite Paris Saclay; Universite de Rennes
摘要：The celebrated Nualart-Peccati criterion [Ann. Probab. 33 (2005) 177-193] ensures the convergence in distribution toward a standard Gaussian random variable N of a given sequence {X-n}(n >= 1) of multiple Wiener-Ito integrals of fixed order, if E[X-n(2)] -> 1 and E[X-n(4)] -> E[N-4] = 3. Since its appearance in 2005, the natural question of ascertaining which other moments can replace the fourth moment in the above criterion has remained entirely open. Based on the technique recently introduce...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for the parabolic Anderson equation {partial derivative u/partial derivative t (t, x) = 1/2 Delta u(t, x) + V (t, x)u(t, x), u(0, x) = u(0)(x), where the homogeneous generalized Gaussian noise V (t, x) is, among other forms, white or fractional white ...
