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作者：Gouezel, Sebastien
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is known since the work of Ancona and Gouezel-Lalley that the Martin boundary coincides with the geometric boundary. The goal of this paper is to weaken the finite support assumption. We first show that, in any nonamenable group, there exist probability measures...
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作者：Denisov, Denis; Wachtel, Vitali
作者单位：University of Manchester; University of Munich
摘要：We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Browni...
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作者：Chen, Le; Dalang, Robert C.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but this measure may also have noncompact support and even be nontempered (e.g., with exponentially growing tails). Existence and uniqueness of a random field solution is proved without appealing to Gronwall's lemma, by keeping tight control over m...
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作者：Lubetzky, Eyal; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes Etudes Sci. Publ. Math. 90 (1999) 5-43], it was there shown to be governed by the first level of Fourier coefficients in the central case of monotone functions at a constant critical probability p(c). Here we study noise sensitivity and a natural stronger version of it, addressing the effect of noise gi...
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作者：Gravner, Janko; Holroyd, Alexander E.
作者单位：University of California System; University of California Davis; Microsoft
摘要：We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random initial seed on an interval of length L, with probability tending to one as L -> infinity, the evolution is a replicator. That is, a region of space time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of oth...
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作者：Neininger, Ralph; Sulzbach, Henning
作者单位：Goethe University Frankfurt
摘要：Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to the space C[0, 1] of continuous functions endowed with uniform topology and the space D[0, 1] of cadlag functions with the Skorokhod topology. The contraction method originated from the probabilistic analysis of algorithms and random trees where characterist...
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作者：Janson, Svante; Stefansson, Sigurdur Orn
作者单位：Uppsala University; Royal Institute of Technology; Nordic Institute for Theoretical Physics; Stockholm University
摘要：We study random bipartite planar maps defined by assigning nonnegative weights to each face of a map. We prove that for certain choices of weights a unique large face, having degree proportional to the total number of edges in the maps, appears when the maps are large. It is furthermore shown that as the number of edges n of the planar maps goes to infinity, the profile of distances to a marked vertex rescaled by n(-1/2) is described by a Brownian excursion. The planar maps, with the graph met...
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作者：Khoshnevis, Davar; Xiao, Yimin
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W (E) boolean AND F, where E subset of (0, infinity) and F subset of R-d are arbitrary nonrandom compact sets. Our formula is related intimately to the thermal capacity of Watson [Proc. Lond. Math. Soc. (3) 37 (1978) 342-362]. We prove also that when d >= 2, our formula can be described in terms of the Hausdorff dimension of E x F, where E x F is viewed as a subspace of ...
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作者：Cox, A. M. G.; Peskir, G.
作者单位：University of Bath; University of Manchester
摘要：We present a constructive probabilistic proof of the fact that if B = (B-t)(t >= 0) is standard Brownian motion started at 0, and mu is a given probability measure on R such that mu({0}) = 0, then there exists a unique left-continuous increasing function b: (0, infinity) -> R boolean OR {+infinity} and a unique left-continuous decreasing function c: (0, infinity) -> R boolean OR (-infinity) such that B stopped at tau(b,c) = inf{t > 0 vertical bar B-t >= b(t) or B-t <= c(t)} has the law p,. The...
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作者：Jiang, Tiefeng; Matsumoto, Sho
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Nagoya University
摘要：Let theta(1) ,..., theta(n) be random variables from Dyson's circular beta-ensemble with probability density function Const. Pi(1 <= j<= n) vertical bar e(i theta j) - e(i theta k)vertical bar(beta). For each n >= 2 and beta > 0, we obtain some inequalities on E[p(mu)(Z(n))<(P-v(Z(n)))over bar>], where Z(n) = (e(i theta 1) ,..., e(i theta n)) and p(mu) is the power-sum symmetric function for partition mu. When beta = 2, our inequalities recover an identity by Diaconis and Evans for Haar-invari...
