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作者：Kabluchko, Zakhar; Klimovsky, Anton
作者单位：Ulm University; Leiden University; Leiden University - Excl LUMC
摘要：The partition function of the random energy model at inverse temperature is a sum of random exponentials , where are independent real standard normal random variables (=random energies), and . We study the large N limit of the partition function viewed as an analytic function of the complex variable . We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the ra...
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作者：Gamarnik, David
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The paper is devoted to the problem of establishing right-convergence of sparse random graphs. This concerns the convergence of the logarithm of number of homomorphisms from graphs or hyper-graphs to some target graph . The theory of dense graph convergence, including random dense graphs, is now well understood (Borgs et al. in Ann Math 176:151-219, 2012; Borgs et al. in Adv Math 219:1801-1851, 2008; Chatterjee and Varadhan in Eur J Comb 32:1000-1017, 2011; Lovasz and Szegedy in J Comb Theory ...
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作者：Barbour, A. D.; Kowalski, E.; Nikeghbali, A.
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law (without normalization) cannot be expected. The setting is one in which the simplest approximation to the -th random variable is by a particular member of a given family of distributions, whose variance increases with . The basic assumption is that the ratio of the characteristic function of to that of converges to a limit in a prescribed fas...
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作者：Lacoin, Hubert
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we study the abundance of self-avoiding paths of a given length on a supercritical percolation cluster on . More precisely, we count , the number of self-avoiding paths of length on the infinite cluster starting from the origin (which we condition to be in the cluster). We are interested in estimating the upper growth rate of , , which we call the connective constant of the dilute lattice. After proving that this connective constant is a.s. non-random, we focus on the two-dimens...
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作者：Espinasse, T.; Gamboa, F.; Loubes, J-M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper, using spectral theory of Hilbertian operators, we study a special class of Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their asymptotic optimality.
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作者：Grimmett, Geoffrey R.; Manolescu, Ioan
作者单位：University of Cambridge
摘要：In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the se...
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作者：Austin, Tim; Panchenko, Dmitry
作者单位：New York University; Texas A&M University System; Texas A&M University College Station
摘要：We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.
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作者：Bertini, Lorenzo; Giacomin, Giambattista; Poquet, Christophe
作者单位：Sapienza University Rome; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
摘要：We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition at a critical value of the interaction strength parameter K, in the limit of the number N of rotators going to infinity. A Fokker-Planck PDE captures the evolution of the empirical measure of the system as N ->infinity, at least for finite times and when the empirical measure of the system at time...
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作者：Burdzy, Krzysztof; Scheutzow, Michael
作者单位：University of Washington; University of Washington Seattle; Technical University of Berlin
摘要：We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at . We show that these processes do not have to have the distribution of standard Brownian motion in the backward direction of time, no matter which random time we take as the origin. We study the maximum and minimum rates of growth for these processes in the backward direction. We also address the question of which ext...
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作者：Burdzy, Krzysztof; Nualart, David; Swanson, Jason
作者单位：University of Washington; University of Washington Seattle; University of Kansas; State University System of Florida; University of Central Florida
摘要：The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter . We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.
