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作者：Basak, Anirban; Dembo, Amir
作者单位：Duke University; Stanford University; Stanford University
摘要：We consider the ferromagnetic Ising model on a sequence of graphs G(n) converging locally weakly to a rooted random tree. Generalizing [Probab. Theory Related Fields 152 (2012) 31-51], under an appropriate continuity property, we show that the Ising measures on these graphs converge locally weakly to a measure, which is obtained by first picking a random tree, and then the symmetric mixture of Ising measures with + and -boundary conditions on that tree. Under the extra assumptions that G(n) ar...
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作者：Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Given some essentially separable filtration (Zn)(n <= 0) indexed by the non-positive integers, we define the notion of complementability for the filtrations contained in (Zn)(n <= 0). We also define and characterize the notion ofmaximality for the poly-adic sub-filtrations of (Zn)(n <= 0). We show that any poly-adic sub-filtration of (Zn)(n <= 0) which can be complemented by a Kolmogorovian filtration is maximal in (Zn)(n <= 0). We show that the converse is false, and we prove a partial conver...
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作者：Li, Xinyi
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider simple random walk on Z(d), d >= 3. Motivated by the work of A.-S. Sznitman and the author in [Probab. Theory Related Fields 161 (2015) 309-350] and [Electron. J. Probab. 19 (2014) 1-26], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk. We derive asymptotic lower bounds that bring into play random interlacements. Although open at the moment, some of the lower bounds we o...
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作者：Tikhomirov, Konstantin; Youssef, Pierre
作者单位：University of Alberta
摘要：We connect this question to a problem of estimating the probability that the image of certain random matrices does not intersect with a subset of the unit sphere Sn-1. In this way, the case of a discretized Brownian motion is related to Gordon's escape theorem dealing with standard Gaussian matrices. We show that for the random walk BMn(i), i is an element of N, the convex hull of the first C-n steps (for a sufficiently large universal constant C) contains the origin with probability close to ...
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作者：Dembo, Amir; Montanari, Andrea; Sen, Subhabrata
作者单位：Stanford University; Stanford University; Stanford University
摘要：For Erdos-Renyi random graphs with average degree gamma, and uniformly random gamma-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are n(gamma/4 + P-* root gamma/4 + o(root gamma)) + o(n) while the size of the minimum bisection is n(gamma/4 - P-* root gamma/4 + o(root gamma)) + o(n). Our derivation relates the free energy of the anti-ferromagnetic Ising model on such graphs to that of the SherringtonKirkpatrick model, with P-...
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作者：Krokowski, Kai; Reichenbachs, Anselm; Thaele, Christoph
作者单位：Ruhr University Bochum
摘要：A new Berry-Esseen bound for nonlinear functionals of nonsymmetric and nonhomogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete Ornstein-Uhlenbeck semigroup. The result is applied to subgraph counts and to the number of vertices having a prescribed degree in the Erd os-Renyi random graph. A further application deals with a percolation problem on trees.
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作者：Flandoli, Franco; Gess, Benjamin; Scheutzow, Michael
作者单位：University of Pisa; Max Planck Society; Technical University of Berlin
摘要：We provide sufficient conditions for weak synchronization/stabilization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single random point. This generalizes previous results in two directions: First, we do not restrict to Banach spaces, and second, we do not require the partial order to be admissible nor normal. As a second main result and application, we prove weak synchr...
