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On the span of Brownian motion in a field in one dimension

โœ Scribed by Yu.A. Makhnovskii; M.E. Maslova; A.M. Berezhkovskii

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
560 KB
Volume
225
Category
Article
ISSN
0378-4371

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โœฆ Synopsis

We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the probability density for the span together with the first two moments. Our results indicate that at very short times the dominant effect is diffusion while at very long times the field plays the dominant role.

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