منابع مشابه
Range of a Transient 2d-Random Walk
We study the range of a planar random walk on a randomly oriented lattice, already known to be transient. We prove that the expectation of the range grows linearly, in both the quenched (for a.e. orientation) and annealed (”averaged”) cases. We also express the rate of growth in terms of the quenched Green function and eventually prove a weak law of large numbers in the (non-Markovian) annealed...
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We prove strong theorems for the local time at in nity of a nearest neighbor transient random walk. First, laws of the iterated logarithm are given for the large values of the local time. Then we investigate the length of intervals over which the walk runs through (always from left to right) without ever returning. AMS 2000 Subject Classi cation: Primary 60G50; Secondary 60F15, 60J55.
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Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
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We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z. This endeavor solves a problem of Barlow and Taylor (1991).
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We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (Xn) has positive or zero speed according to some positive parameter α > 1 or ≤ 1. In this article, we give the exact rate of growth of (Xn) in the zero speed regime, namely: for 0 < α < 1, Xn/n α+1 2 converges in law to a Mittag-Leffler distribution whereas for α = 1, Xn(...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1973
ISSN: 0304-4149
DOI: 10.1016/0304-4149(73)90031-8