## Search

Now showing items 1-10 of 10

#### 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 ...

#### The sharp phase transition for level set percolation of smooth planar Gaussian fields

We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase transition in Bernoulli percolation. ...

#### On the number of excursion sets of planar Gaussian fields

The Nazarov-Sodin constant describes the average number of nodal set components of Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary ...

#### 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 ...

#### 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. ...

#### 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 ...

#### 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. ...

#### 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 ...