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Aurzada, F. and Simon, T. (2015) Persistence Probabilities and Exponents. In: Lévy Matters V, Springer, Berlin, 183-224.
https://doi.org/10.1007/978-3-319-23138-9_3

has been cited by the following article:

• TITLE: Persistence Exponent for the Simple Diffusion Equation: The Exact Solution for Any Integer Dimension

  AUTHORS: Devashish Sanyal

  KEYWORDS: Non-Equilibrium Statistical Mechanics, Diffusion Equation, Persistence Exponent, Probability Theory

  JOURNAL NAME: Journal of Modern Physics, Vol.12 No.10, August 4, 2021

  ABSTRACT: The persistence exponent for the simple diffusion equation , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field at a specified spatial coordinate remains positive throughout for a certain time t behaves as for asymptotically large time t. The value of , calculated here for any integer dimension d, is for and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values for respectively.