Persistence exponent of the diffusion equation in epsilon dimensions
Statistical Mechanics
2010-08-26 v1
Abstract
We consider the d-dimensional diffusion equation for a field phi(x,t) with random initial condition, and observe that, when appropriately scaled, phi(0,t) is Gaussian and Markovian in the limit d->0. This leads via the Majumdar-Sire perturbation theory to a small-d expansion for the persistence exponent theta(d). We find theta(d) = d/4 - 0.12065...d^{3/2} + ...
Cite
@article{arxiv.cond-mat/9911138,
title = {Persistence exponent of the diffusion equation in epsilon dimensions},
author = {H. J. Hilhorst},
journal= {arXiv preprint arXiv:cond-mat/9911138},
year = {2010}
}
Comments
4 pages, latex, no figures