Critical dimensions of the diffusion equation

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.

4 pages, 5 figures

References in corpus (8)

• Persistence exponents for fluctuating interfaces
• Large deviations and nontrivial exponents in coarsening systems
• Diffusive persistence and the `sign-time' distribution
• Residence Time Distribution for a Class of Gaussian Markov Processes
• Generalized persistence exponents: an exactly soluble model
• Sign-time distributions for interface growth
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• Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation
• Exact persistence exponent for the $2d$-diffusion equation and related Kac polynomials
• Persistence Exponents and the Statistics of Crossings and Occupation Times for Gaussian Stationary Processes
• Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation
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• Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks
• Series Expansion Calculation of Persistence Exponents
• Statistics of the occupation time for a random walk in the presence of a moving boundary
• The effect of shear on persistence in coarsening systems
• Survival exponents for some Gaussian processes