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Now showing items 1-8 of 8

#### 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 ...

#### Two-site localisation in the Bouchaud trap model with slowly varying traps

(Institute of Mathematical Statistics, 2015-03-07)

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. ...

#### Functional limit theorems for the Bouchaud trap model with slowly varying traps

(Elsevier, 2014-12-19)

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 ...

#### A new phase transition in the parabolic Anderson model with partially duplicated potential

(Elsevier, 2018-12-19)

We investigate a variant of the parabolic Anderson model, introduced in previous work, in which an i.i.d. potential is partially duplicated in a symmetric way about the origin, with each potential value duplicated independently ...

#### Quenched localisation in the Bouchaud trap model with regularly varying traps

(2016-03)

This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily ...

#### Quenched localisation in the Bouchaud trap model with slowly varying traps

(Springer Verlag, 2016-04-27)

We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each $N \in \{2, 3, \ldots\}$ ...

#### Localisation in the Bouchaud-Anderson Model

(Elsevier, 2016-05-11)

It is well-known that both branching random walk models and trap models can exhibit intermittency and localisation phenomena; the prototypical examples being the parabolic Anderson and Bouchaud trap models respectively. ...

#### Delocalising the parabolic Anderson model through partial duplication of the potential

(Springer Verlag, 2017-09-06)

The parabolic Anderson model on $\mathbb{Z}^d$ with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification ...