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Persistence exponent of the diffusion equation in epsilon dimensions

H. J. Hilhorst
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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} + ...

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H. J. Hilhorst. 1999-11-10. Persistence exponent of the diffusion equation in epsilon dimensions. https://doi.org/10.1016/s0378-4371(99)00509-9

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