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作者：Puhalskii, AA
作者单位：University of Colorado System; University of Colorado Denver
摘要：We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components and of the numbers of the excess edges of the giant components. For the supercritical case, we obtain the asymptotics of normal deviations and the logarithmic asymptotics of lar...
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作者：Duquesne, T
作者单位：Universite Paris Saclay
摘要：Let b be an integer greater than I and let W-epsilon = (W-n(epsilon); n > 0) be a random walk on the b-ary rooted tree U-b, starting at the root, going up (resp. down) with probability 1/2 + epsilon (resp. 1/2 - epsilon), epsilon is an element of (0, 1/2), and choosing direction i epsilon {1,...,b) when going up with probability a(i). Here a = (a(1),...,a(b)) stands for some nondegenerated fixed set of weights. We consider the range {W-n(epsilon); n >= 0} that is a subtree Of U-b. It correspon...
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作者：Konstantinides, DG; Mikosch, T
作者单位：University of Aegean; University of Copenhagen
摘要：In this paper we consider the stochastic recurrence equation Y-t = A(t)Y(t-1) + B-t for an i.i.d. sequence of pairs (A(t), B-t) of nonnegative random variables, where we assume that Bt is regularly varying with index kappa > 0 and EA(t)(kappa) < 1. We show that the stationary solution (Y-t) to this equation has regularly varying finite-dimensional distributions with index K. This implies that the partial sums S-n = Y-1 + - - - + Y-n of this process are regularly varying. In particular, the rel...
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作者：Boucheron, S; Bousquet, O; Lugosi, G; Massart, P
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Max Planck Society; Pompeu Fabra University; Universite Paris Saclay
摘要：A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Anti. Probab. 31 (2003) 1583-1614], and is based on a generalized tensorization inequality due to Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168]. The new inequalities prove to be a versatile tool in a wide range o...
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作者：Anshelevich, M
作者单位：University of California System; University of California Riverside
摘要：Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom, we calculate and give an interpretation of linearization coefficients for a number of polynomial families. Th...
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作者：Holroyd, AE; Peres, Y
作者单位：University of British Columbia; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Let Pi be an ergodic simple point process on R-d and let Pi* be its Palm version. Thorisson [Ann. Probab. 24 (1996) 2057-2064] proved that there exists a shift coupling of Pi and Pi*; that is, one can select a (random) point Y of Pi such that translating Pi by -Y yields a configuration whose law is that of Pi*. We construct shift couplings in which Y and Pi* are functions of Pi and prove that there is no shift coupling in which Pi is a function of Pi*. The key ingredient is a deterministic tra...
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作者：Hsing, T; Rootzén, H
作者单位：University System of Ohio; Ohio State University; Chalmers University of Technology
摘要：This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X-1,..., X-Nn where X-1, X-2,... are i.i.d. in R-2 with distribution F and N-n is independent of the X-i and satisfies N-n/n --> (p) 1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded support. The general results are applied to a number of special cases, including elliptically co...
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作者：Borgs, C; Chayes, JT; Van der Hofstad, R; Slade, G; Spencer, J
作者单位：Microsoft; University of British Columbia; Eindhoven University of Technology; New York University
摘要：In a previous paper we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and showed that this triangle condition implies that the percolation phase transition has many features in common with the phase transition on the complete graph. In this paper we use a new and simplified approach to the lace expansion to prove quite generally that, for finite graphs that are tori, the triangle condition fo...
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作者：Nikeghbali, A; Yor, M
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Recently, Williams [Bull. London Math. Soc. 34 (2002) 610-612]gave an explicit example of a random time rho associated with Brownian motion such that p is not a stopping time but EM rho = EM0 for every bounded martingale M. The aim of this paper is to characterize such random times, which we call pseudo-stopping times, and to construct further examples, using techniques of progressive enlargements of filtrations.
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作者：Léandre, R
作者单位：Universite Bourgogne Europe
摘要：We give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the Chen-Souriau sense and to establish a link with cyclic cohomology. With the second one, we can establish a stochastic fixed point theorem.
