Random walks on lattices with points of two colors. II: Some rigorous inequalities for symmetric random walks
type: Item
instance of: scholarly article
title: Random walks on lattices with points of two colors. II: Some rigorous inequalities for symmetric random walks
zbMATH Open document ID: 0659.60099
DOI: 10.1007/BF01007973
author: F. den Hollander
author: P. W. Kasteleyn
published in: Journal of Statistical Physics
publication date: 1985-01-01T00:00:00Z
review text: [For part I, see the preceding review, Zbl 0659.60098]. We continue our investigation of a model of random walks on lattices with two kinds of points, ``black'' and ``white''. The colors of the points are stochastic variables with a translation-invariant, but otherwise arbitrary, joint probability distribution. The steps of the random walk are independent of the colors. We are interested in the stochastic properties of the sequence of consecutive colors encountered by the walker. In this paper we first summarize and extend our earlier general results. Then, under the restriction that the random walk be symmetric, we derive a set of rigorous inequalities for the average length of the subwalk from the starting point to a first black point and of the subwalks between black points visited in succession. A remarkable difference in behavior is found between subwalks following an odd-numbered and subwalks following an even-numbered visit to a black point. The results can be applied to a trapping problem by identifying the black points with imperfect traps.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4078431
zbMATH Keywords: average length of successive runs
zbMATH Keywords: ergodic theorems
zbMATH Keywords: perfect and imperfect traps
zbMATH Keywords: random walks on lattices
zbMATH Keywords: inequalities
zbMATH Keywords: trapping problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4078431