Persistence exponent of the diffusion equation in ε dimensions

H.j Hilhorst

Physica A: Statistical Mechanics and its Applications, 2000, vol. 277, issue 1, 124-126

Abstract: We consider the d-dimensional diffusion equation ∂tφ(x,t)=Δφ(x,t) with random initial condition, and observe that, when appropriately scaled, φ(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 θ(d). We find θ(d)=14d−0.12065…d3/2+⋯

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:277:y:2000:i:1:p:124-126

DOI: 10.1016/S0378-4371(99)00509-9

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