The Pearson walk with shrinking steps in two dimensions
نویسندگان
چکیده
منابع مشابه
The Pearson walk with shrinking steps in two dimensions
We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth step is random and its length equals λN−1, with λ < 1. As λ increases past a critical value λc, the endpoint distribution in two dimensions, P (r), changes from having a global maximum away from the origin to being peaked at the origin. The probability distribution for a single coordinate...
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We outline the properties of a symmetric random walk in one dimension in which the length of the nth step equals l, with l,1. As the number of steps N→` , the probability that the end point is at x approaches a limiting distribution Pl(x) that has many beautiful features. For l,1/2, the support of Pl(x) is a Cantor set. For 1/2<l,1, there is a countably infinite set of l values for which Pl(x) ...
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Computer studies of random walks in two dimensions are reported. The concept of degeneracy D is introduced in which only D steps are allowed at any one lattice point. Properties of the probability distribution function for the distance covered in N steps are discussed. The lifetime of a walk of degeneracy D is also examined. (Submitted to Journal of Mathematical Physics .) * -Work supported by ...
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ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2010
ISSN: 1742-5468
DOI: 10.1088/1742-5468/2010/01/p01006