Consider a random walk in one dimension. In a single step the probability of a displacement between

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Consider a random walk in one dimension. In a single step the probability of a displacement between x and x + dx is given by

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After N steps the displacement of the walker is SX++XN, where X, is the displacement during the ith step. Assume the steps are independent of one another. After N steps,

(a) what is the probability density for the displacement, S, of the walker and

(b) what are the average displacement, (S), and the standard deviation of the walker?

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A Modern Course In Statistical Physics

ISBN: 9780471595205

2nd Edition

Authors: Linda E. Reichl

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Question Posted: Sep 18, 2024 08:00 AM

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Consider a random walk in one dimension. In a single step the probability of a displacement between

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1 (x-a)) P(x)dx exp 2O 202

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A Modern Course In Statistical Physics

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