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Now showing items 1-8 of 8

#### On the distribution of maximum value of the characteristic polynomial of GUE random matrices

Motivated by recently discovered relations between logarithmically correlated Gaussian processes and characteristic polynomials of large random $N \times N$ matrices $H$ from the Gaussian Unitary Ensemble (GUE), we consider ...

#### 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. ...

#### 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 $N \in \{2, 3, \ldots\}$ ...

#### 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. ...

#### 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 ...

#### 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 ...