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作者：Berestycki, Nathanael; Durrett, Rick
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Cornell University
摘要：Our work is motivated by Bourque and Pevzner's (2002) simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising result about the random transposition walk on the group of permutations on n elements. Consider this walk in continuous time starting at the identity and let D-t be the minimum number of transpositions needed to go back to the identity from the location at time t. D (t) undergoes a phase transition: the distance D-cn /2 ...
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作者：Collevecchio, Andrea
作者单位：G d'Annunzio University of Chieti-Pescara
摘要：Consider a linearly edge-reinforced random walk defined on the b-ary tree, b >= 70. We prove the strong law of large numbers for the distance of this process from the root. We give a sufficient condition for this strong law to hold for general edge-reinforced random walks and random walks in a random environment. We also provide a central limit theorem.
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作者：Dubédat, J
作者单位：New York University
摘要：It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if kappa > 4 and a.s. cutpoints if 4 < kappa < 8. If kappa > 4, an appropriate version of SLE(kappa) has a renewal property: it starts afresh after visiting its frontier. Thus one call give an excursion decomposition for this particular SLE(kappa) away from its frontier. For 4 < kappa < 8, there is a two-sided analogue of this situation: a particular version of SLE(K) has a renewal property w.r.t its cutpoints; one st...
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作者：Khoshnevisan, D; Levin, DA; Méndez-Hernández, PJ
作者单位：Utah System of Higher Education; University of Utah; Universidad Costa Rica
摘要：Consider a sequence (X-i(0)}(i=1)(n) of i.i.d. random variables. Associate to each Xi (0) an independent mean-one Poisson clock. Every time a clock rings replace that X-variable by an independent copy and restart the clock. In this way, we obtain i.i.d. stationary processes {X-i(t)}(t >= 0) (i = 1, 2,..) whose invariant distribution is the law nu of X-1 (0). Benjamini et al. (2003) introduced the dynamical walk S-n (t) = X-1 (t) +...+ X-n(t), and proved among other things that the LIL holds fo...
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作者：Bartlett, PL; Mendelson, S
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Australian National University
摘要：We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp....
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作者：Balogh, J; Bollobás, B
作者单位：University System of Ohio; Ohio State University; University of Memphis; University of Cambridge
摘要：In the bootstrap percolation on the n-dimensional hypercube, in the initial position each of the 2(n) sites is occupied with probability p and empty with probability 1 - p, independently of the state of the other sites. Every occupied site remains occupied for ever, while an empty site becomes occupied if at least two of its neighbours are occupied. If at the end of the process every site is occupied, we say that the ( initial) position spans the hypercube. We shall show that there are constan...
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作者：Fontes, LRG; Mathieu, P
作者单位：Aix-Marseille Universite
摘要：We study models of continuous time, symmetric, Z(d)-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We consider the case of independent conductances with a polynomial tail near 0 and obtain precise asymptotics for the annealed return probability and convergence times for the random walk confined to a finite box.
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作者：Anderson, GW; Zeitouni, O
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poincare type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wi...
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作者：Gnedin, Alexander; Pitman, Jim; Yor, Marc
作者单位：Utrecht University; University of California System; University of California Berkeley; Sorbonne Universite
摘要：For (R) over tilde = 1-exp(-R) a random closed set obtained by exponential transformation of the closed range R of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of (R) over tilde. We focus on the number of parts K-n of the composition when (R) over tilde is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit the...
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作者：Bass, RF; Chen, ZQ
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Let Z(t)(j), j = 1,..., d, be independent one-dimensional symmetric stable processes of index alpha is an element of (0, 2). We consider the system of stochastic differential equations dX(t)(i) = Sigma(d)(j=1) A(ij)(Xt-)dZ(t)(j), i = 1,...,d, where the matrix A(x) = (A(ij) (x))(1 <= i, j <= d) is continuous and bounded in x and nondegenerate for each x. We prove existence and uniqueness of a weak solution to this system. The approach of this paper uses the martingale problem method. For this, ...
