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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study the upper tail behaviors of the local times of the additive stable processes. Let X-1 (t),..., X-p(t) be independent, d-dimensional symmetric stable processes with stable index 0 < alpha <= 2 and consider the additive stable process (X) over bar (t(1),..., t(p)) = X-1 (t(1)) + ... + X-p (t(p)). Under the condition d < alpha p, we obtain a precise form of the large deviation principle for the local time n(x)([0, t](p)) = integral(t)(o) ... integral(t)(o) delta(x)(X-1(s(1)) + ... + X-p ...
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作者：Pinsky, Ross G.
作者单位：Technion Israel Institute of Technology
摘要：Let the random variable Z(n,k) denote the number of increasing subsequences of length k in a random permutation from S-n, the symmetric group of permutations of { 1,..., n }. In a recent paper [Random Structures Algorithms 29 (2006) 277-295] we showed that the weak law of large numbers holds for Z(n,kn,) if k(n) = o(n(2/5)); that is, lim(n ->infinity) Z (n,kn)/EZ(n,kn) = 1 in probability. The method of proof employed there used the second moment method and demonstrated that this method cannot ...
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作者：Dembo, Amir; Peres, Yuval; Rosen, Jay
作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We show that the largest disccovered by a simple random walk (SRW) on Z(2) after n steps has radius n(1/4+o(1)), thus resolving an open problem of Revesz [Random Walk in Random and Non-Random Environments (1990) World Scientific, Teaneck, NJ]. For any fixed , the largest disc completely covered at least times by the SRW also has radius n(1/4+o(l)). However, the largest disc completely covered by each of E independent simple random walks on Z(2) after n steps is only of radius n (1/(2+2 root)+o...
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作者：Brossard, Jean; Leuridan, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
