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Functional limit theorems for the Bouchaud trap model with slowly varying traps
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous ...
Complete Localisation and Exponential Shape of the Parabolic Anderson Model with Weibull Potential Field
(Institute of Mathematical Statistics, 2014-07)
We consider the parabolic Anderson model with Weibull potential field, for all values of the Weibull parameter. We prove that the solution is eventually localised at a single site with overwhelming probability (complete ...