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作者：Gayrard, Veronique
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider Metropolis dynamics of the Random Energy Model. We prove that the classical two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. To do this we link the two-time correlation function to a certain continuous-time clock process which, after proper rescaling, is...
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作者：Addario-Berry, Louigi
作者单位：McGill University
摘要：This work proves new probability bounds relating to the height, width, and size of Galton-Watson trees. For example, if T is any Galton-Watson tree, and H, W, and |T| are the height, width, and size of T, respectively, then H/W has sub-exponential tails and H/|T|1/2 has sub-Gaussian tails. Although our methods apply without any assumptions on the offspring distribution, when information is provided about the distribution the method can be adapted accordingly, and always seems to yield tight bo...
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作者：Cox, Alexander M. G.; Obloj, Jan; Touzi, Nizar
作者单位：University of Bath; University of Oxford; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time-...
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作者：Epstein, Charles L.; Pop, Camelia A.
作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
摘要：We provide a detailed description of the structure of the transition probabilities and of the hitting distributions on boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes that we study are a generalization of the classical Wright-Fisher process. The main ingredients in our proofs are based on the analysis of the regularity properties of solutions to a forward Kolmogorov equation defined on a compact manifold...
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作者：Aggarwal, Amol
摘要：In this paper we consider NxN real generalized Wigner matrices whose entries are only assumed to have finite (2+epsilon)th moment for some fixed, but arbitrarily small, epsilon>0. We show that the Stieltjes transforms mN(z) of these matrices satisfy a weak local semicircle law on the nearly smallest possible scale, when =I(z) is almost of order N-1. As a consequence, we establish bulk universality for local spectral statistics of these matrices at fixed energy levels, both in terms of eigenval...
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作者：Hutchcroft, Tom; Peres, Yuval
作者单位：University of Cambridge; Microsoft
摘要：We prove that the uniform spanning forests of Z(d) and Z(l) have qualitatively different connectivity properties whenever l > d >= 4. In particular, we consider the graph formed by contracting each tree of the uniform spanning forest down to a single vertex, which we call the component graph. We introduce the notion of ubiquitous subgraphs and show that the set of ubiquitous subgraphs of the component graph changes whenever the dimension changes and is above 8. To separate dimensions 5, 6, 7, ...
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作者：Erschler, Anna
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the neighborhoods of a typical point Zn visited at n-th step of a random walk, determined by the condition that the transition probabilities stay close to n(Zn). If such neighborhood contains a ball of radius Cn, we say that the random walk has almost invariant transition probabilities. We prove that simple random walks on wreath products of Z with finite groups have almost invariant distributions. A weaker version of almost invariance implies a necessary condition of Ozawa's criterio...
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作者：Boutillier, Cedric; de Tiliere, Beatrice; Raschel, Kilian
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite de Tours
摘要：The Z-invariant Ising model(Baxter in Philos Trans R Soc Lond A Math Phys Eng Sci 289(1359):315-346, 1978) is defined on an isoradial graph and has coupling constants depending on an elliptic parameter k. When k=0 the model is critical, and as k varies the whole range of temperatures is covered. In this paper we study the corresponding dimer model on the Fisher graph, thus extending our papers(Boutillier and de Tiliere in Probab Theory Relat Fields 147:379-413, 2010; Commun Math Phys 301(2):47...
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作者：Lambert, Gaultier; Paquette, Elliot
作者单位：University of Zurich; University System of Ohio; Ohio State University
摘要：We compute the leading asymptotics as N of the maximum of the field QN(q)=log|q-AN|,qC, for any unitarily invariant Hermitian random matrix AN associated to a non-critical real-analytic potential. Hence, we verify the leading order in a conjecture ofFyodorov and Simm (Nonlinearity 29:2837, 2016. arXiv:1503.07110 [math-ph]) formulated for the GUE. The method relies on a classical upper-bound and a more sophisticated lower-bound based on a variant of the second-moment method which exploits the h...
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作者：Gravner, Janko; Holroyd, Alexander E.
作者单位：University of California System; University of California Davis; University of Washington; University of Washington Seattle
摘要：In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q. At subsequent steps, a vertex becomes occupied if it is not closed and it has at least r occupied neighbors. On the cubic lattice Z(d) of dimension d >= 3 with threshold r = 2, we prove that the final density of occupied sites converges to 1 as p and q both approach 0, regardless of their relative scaling. Our result partially resol...
