The excited random walk in one dimension
نویسندگان
چکیده
منابع مشابه
The 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 کاملCentral Limit Theorem for the Excited Random Walk in Dimension
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d ≥ 2.
متن کاملExcited 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 کاملThe Random Average Process and Random Walk in a Space-time Random Environment in One Dimension
We study space-time fluctuations around a characteristic line for a onedimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n where n is the ratio of macroscopic and microscopic sc...
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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: Journal of Physics A: Mathematical and General
سال: 2005
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/38/12/002