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作者：Deligiannidis, George; Utev, Sergey
作者单位：University of Oxford; University of Nottingham
摘要：Let X-1, X-2, ... be a centred sequence of weakly stationary random variables with spectral measure F and partial sums S-n = X-1 + ... + X-n. We show that var(S-n) is regularly varying of index gamma at infinity, if and only if G(x) := integral(x)(-x) F(dx) is regularly varying of index 2 - gamma at the origin (0 < gamma < 2).
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作者：Grimmett, Geoffrey R.; Manolescu, Joan
作者单位：University of Cambridge
摘要：All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star triangle transformation and the box-crossing property. The exponents in question are the one-arm exponent rho, the 2j-alternating-arms exponents rho(2j) for j >= 1, the volume exponent delta, and the connectivity exponent et...
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作者：Tan, Xiaolu; Touzi, Nizar
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. Our first main result is an extension of the Kantorovitch duality to this context. We also suggest a ...
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作者：Meyerovitch, Tom
作者单位：Ben-Gurion University of the Negev
摘要：In this paper we study the Poisson process over a a-finite measure-space equipped with a measure preserving transformation or a group of measure preserving transformations. For a measure-preserving transformation T acting on a a-finite measure-space X, the Poisson suspension of T is the associated probability preserving transformation T-* which acts on realization of the Poisson process over X. We prove ergodicity of the Poisson-product T x T-* under the assumption that T is ergodic and conser...
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
摘要：We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Szekely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of the manipulations of Fourier transforms used in the original work, we use elementary inequalities for ...
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作者：Roberts, Matthew I.
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.
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作者：Srivastava, Nikhil; Vershynin, Roman
作者单位：Institute for Advanced Study - USA; University of Michigan System; University of Michigan
摘要：We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2 + epsilon moments outside the sphere of radius O(root k). In the specific case of log-concave distributions, this result provides an alternative approach to the Kannan-L...
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作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：The main results in this paper are about the full coalescence time C of a system of coalescing random walks over a finite graph G. Letting m(G) denote the mean meeting time of two such walkers, we give sufficient conditions under which E[C] approximate to 2m(G) and C/m(G) has approximately the same law as in the mean field setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than m(G); th...
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作者：Ledrappier, Francois
作者单位：University of Notre Dame; Sorbonne Universite
摘要：We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.
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作者：Lee, James R.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; Microsoft
摘要：We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic mappings taking values in a Hilbert space. For the special case of discrete, amenable groups, we present a more explicit proof of the Mok-Korevaar-Schoen theorem on the existence of such harmonic maps by constructing them from the heat flow on a Folner set.
