منابع مشابه
Excited Random Walk
A random walk on Z is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on Z is transient iff d > 1. 1. Excited Random Walk A random walk on Z is excited (with bias ε/d) if the first time it visits a vertex it steps right with probability (1 + ε)...
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Following Lyons (1990, [4]) we define a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric networks.
متن کاملCritical Random Walk in Random Environment on Trees
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges of a tree Γ are i.i.d. random variables whose logarithms have mean zero and finite variance. Then the resulting RWRE is transient if simple random walk on Γ...
متن کاملThe excited random walk in one dimension
We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q = 1−p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scal...
متن کاملExcited Random Walk in a Markovian Environment
One dimensional excited random walk has been extensively studied for bounded, i.i.d. cookie environments. In this case, many important properties of the walk including transience or recurrence, positivity or non-positivity of the speed, and the limiting distribution of the position of the walker are all characterized by a single parameter δ, the total expected drift per site. In the more genera...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2003
ISSN: 1083-6489
DOI: 10.1214/ejp.v8-180