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作者：Bianchi, Alessandra; Bovier, Anton; Ioffe, Dmitry
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bonn; Technion Israel Institute of Technology
摘要：We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a meta-stable set. In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.
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作者：Albeverio, Sergio; Kusuoka, Seiichiro
作者单位：University of Bonn; Kyoto University
摘要：The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular domains are shrinking to graphs. The methods we use are probabilistic ones. For shrinking, we use big potentials, respectively, reflection on the boundary of tubes. We show that there exists a unique limit process, and we characterize the limit process by a second...
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作者：Ding, Jian; Lubetzky, Eyal; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 be the largest component of the Erdos-Renyi random graph G(n, p). The mixing time of random walk on C-1 in the strictly supercritical regime, p = c/n with fixed c > 1, was shown to have order log(2) n by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald. In the critical window, p = (1 + epsilon)/n where lambda = epsilon(3)n is bounded, Nachmias and Peres proved that the mixing time on C-1 is of order n. However, it was unclear how to interpolate between these res...
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作者：Letac, Gerard; Piccioni, Mauro
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sapienza University Rome
摘要：In a recent paper [Statist. Probab. Lett. 78 (2008) 1711-1721] it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function F-2(1). In the present paper we fully exploit a formula due to Thomae [J. Reine Angew. Math. 87 (1879) 26-73] in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on th...
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作者：Liu, Jingchen
作者单位：Columbia University
摘要：This paper develops asymptotic approximations of P(f(T) e(f(t)) dt > b) as b -> infinity for a homogeneous smooth Gaussian random field, f, living on a compact d-dimensional Jordan measurable set T. The integral of an exponent of a Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability P(f(Xi) e(f(t)) dt > b) over...
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作者：Fukushima, Masatoshi; Uemura, Toshihiro
作者单位：University of Osaka; Kansai University
摘要：Let E be a locally compact separable metric space and in be a positive Radon measure on it. Given a nonnegative function k defined on E x E off the diagonal whose anti-symmetric part is assumed to be less singular than the symmetric part, we construct an associated regular lower bounded semi-Dirichlet form eta on L-2(E; m) producing a Hunt process X-0 on E whose jump behaviours are governed by k. For an arbitrary open subset D C E, we also construct a Hunt process X-D,X-0 on D in an analogous ...
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作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.
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作者：Grigor'yan, Alexander; Telcs, Andras
作者单位：University of Bielefeld; Budapest University of Technology & Economics
摘要：We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.
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作者：Sheffield, Scott; Sun, Nike
作者单位：Massachusetts Institute of Technology (MIT); Stanford University
摘要：We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version applies in particular to random lattice paths that have chordal SLE kappa as a scaling limit, with kappa < 8 (nonspace-filling). Existing SLE kappa convergence proofs often begin by showing that the Loewner driving functions of these paths (viewed from infinity) ...
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作者：Dumitriu, Ioana; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to the semicircle law. Moreover, we prove concentration estimates on the number of eigenvalues over progressively smaller intervals. We also show that, with high probability, all the eigenvectors are delocalized.
