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)...
متن کاملBalanced Allocation Through Random Walk
We consider the allocation problem in which $m \leq (1-\ve) dn $ items are to be allocated to $n$ bins with capacity $d$. The items $x_1,x_2,\ldots,x_m$ arrive sequentially and when item $x_i$ arrives it is given two possible bin locations $p_i=h_1(x_i),q_i=h_2(x_i)$ via hash functions $h_1,h_2$. We consider a random walk procedure for inserting items and show that the expected time insertion t...
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...
متن کاملExcited Random Walk against a Wall
We analyze randomwalk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of √
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...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2011
ISSN: 1631-073X
DOI: 10.1016/j.crma.2011.02.018