Critical dimensions of the diffusion equation
classification
❄️ cond-mat.stat-mech
hep-lathep-thnlin.CGphysics.atom-ph
keywords
dimensionscriticaldiffusionpersistencecalculationsequationevolutionexponents
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We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the persistence exponents for low dimensions.
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