Brownian Functionals in Physics and Computer Science

Details Brownian Functionals in Physics and Computer Science Brownian Functionals in Physics and Computer Science

2005-10-04

arxiv.org/abs/cond-mat/0510064v1

Current Science, vol-89, 2076 (2005).

Physics

Condensed Matter

Statistical Mechanics

21 pages, 5 .eps figures included

Scientific paper

This is a brief review on Brownian functionals in one dimension and their various applications, a contribution to the special issue ``The Legacy of Albert Einstein" of Current Science. After a brief description of Einstein's original derivation of the diffusion equation, this article provides a pedagogical introduction to the path integral methods leading to the derivation of the celebrated Feynman-Kac formula. The usefulness of this technique in calculating the statistical properties of Brownian functionals is illustrated with several examples in physics and probability theory, with particular emphasis on applications in computer science. The statistical properties of "first-passage Brownian functionals" and their applications are also discussed.

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