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作者：Goetze, Friedrich; Venker, Martin
作者单位：University of Bielefeld
摘要：We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or determinantal representation, the local correlations in the bulk coincide in the limit of infinitely many particles with those known from random Hermitian matrices; in particular they can be expressed as determinants of the so-called sine kernel. These results m...
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作者：Sly, Allan; Sun, Nike
作者单位：University of California System; University of California Berkeley; Australian National University; Stanford University
摘要：We establish that the normalized log-partition function of any two-spin system on bipartite locally tree-like graphs converges to a limiting free energy density which coincides with the (nonrigorous) Bethe prediction of statistical physics. Using this result, we characterize the local structure of two-spin systems on locally tree-like bipartite expander graphs without the use of the second moment method employed in previous works on these questions. As a consequence, we show that for both the ...
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作者：Bollobas, Bela; Holmgren, Cecilia; Smith, Paul; Uzzell, Andrew J.
作者单位：University of Cambridge; University of Memphis
摘要：Let r is an element of N. In r-neighbour bootstrap percolation on the vertex set of a graph G, vertices are initially infected independently with some probability p. At each time step, the infected set expands by infecting all uninfected vertices that have at least r infected neighbours. When p is close to 1, we study the distribution of the time at which all vertices become infected. Given t = t (n) = o (log n/ log log n), we prove a sharp threshold result for the probability that percolation...
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作者：Cerf, Raphael; Theret, Marie
作者单位：Universite Paris Saclay; Universite Paris Saclay; Universite Paris Cite
摘要：We consider the standard first passage percolation model in the resealed graph Z(d)/n for d >= 2 and a domain Omega of boundary Gamma in R-d Let Gamma(1) and Gamma(2) be two disjoint open subsets of Gamma, representing the parts of Gamma through which some water can enter and escape from Omega. A law of large numbers for the maximal flow from Gamma(1), to Gamma(2) in Omega is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. A maximal...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove that for any constant K >= 1, the value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over K by value functions whose second-order derivatives are bounded by a constant times K. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.
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作者：Miller, Jason; Sun, Nike; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Microsoft
摘要：The conformal loop ensemble CLEK is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plane. The parameter K varies between 8/3 and 8; CLE8/3 is empty while CLE8 is a single space-filling loop. In this work, we study the geometry of the CLE gasket, the set of points not surrounded by any loop of the CLE. We show that the almost sure Hausdorff dimension of the gasket is bounded from below by 2 (8 K)(3K 8)/(32K) when 4...
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作者：Schuhmacher, Dominic; Stucki, Kaspar
作者单位：University of Bern; University of Gottingen
摘要：We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's meth...
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作者：Kifer, Yuri; Varadhan, S. R. S.
作者单位：Hebrew University of Jerusalem; New York University
摘要：We obtain functional central limit theorems for both discrete time expressions of the form 1/root N Sigma([Nt])(n=1) (F(X(q(1)(n)),...,X(q(l)(n))) - (F) over bar) and similar expressions in the continuous time where the sum is replaced by an integral. Here X(n), n >= 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties, (F) over bar = integral F d(mu X ... X mu...
