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Critical dimensions of the diffusion equation

T. J. Newman·Will Loinaz
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Abstract

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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T. J. Newman, Will Loinaz. 2000-09-22. Critical dimensions of the diffusion equation. https://doi.org/10.1103/physrevlett.86.2712

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