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Brownian MotionFluctuations, Dynamics, and Applications$
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Robert M. Mazo

Print publication date: 2008

Print ISBN-13: 9780199556441

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199556441.001.0001

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(p.111) 9 RANDOM WALK
Brownian Motion

Robert M. Mazo

Oxford University Press

This chapter introduces the idea of random walk and studies a number of simple cases to illustrate the concepts, mostly in one dimension. The symmetric Pearson walk, the biased walk, and the persistent walk are treated for lattice walks in discrete time, and the results generalized to continuum walks. Asymptotic results for large number of steps or long times are emphasized. The problems of random walk with boundaries and first passage times are introduced. Remarks on further generalizations and problems are briefly made.

Keywords:   random walk, Pearson walk, lattice walks, Levy, symmetric, biased walk, persistent walk, boundaries, first passage

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