Brownian Functionals in Physics and Computer Science [article]

Satya N. Majumdar
2005 arXiv   pre-print
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
more » ... 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.
arXiv:cond-mat/0510064v1 fatcat:5z6a5b4jynghnb2a4h7m74c35m