Persistence exponent of the diffusion equation in epsilon dimensions
arXiv:cond-mat/9911138 · doi:10.1016/S0378-4371(99)00509-9
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} + ...
4 pages, latex, no figures
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- Critical dimensions of the diffusion equation
- Persistence in a Stationary Time-series
- Distribution of zeros in the rough geometry of fluctuating interfaces