We consider a branching random walk on the lattice, where the branching rates are given by
an iid Pareto random potential. We show that the system of particles, rescaled in an …

We consider a generalization of spatial branching coalescing processes in which the
behaviour of individuals is not (necessarily) independent, on the contrary, individuals tend to …

This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …

We investigate a model of continuous-time simple random walk paths in $\mathbb {Z}^ d $
undergoing two competing interactions: an attractive one towards the large values of a …

The Bouchaud–Anderson model (BAM) is a generalisation of the parabolic and erson model
(PAM) in which the driving simple random walk is replaced by a random walk in an …

The main objective of this thesis is to analyse the dynamical behaviour of different linear and
non-linear stochastic heat equations using analytical and probabilistic techniques. We begin …

In this chapter, we discuss much stronger and more detailed assertions about intermittency
than we did before. They characterise the long-time behaviour of the mass flow through a …

Abstract In Sect. 3.2, we described the heuristics for the large-t exponential rate of the
moments of the total mass U (t), neglecting all technical issues. More precisely, we only gave …

One of the most interesting features of the PAM is that, being a partial differential equation
with random coefficients, it lies in the intersection of probability and functional analysis …

In this section, we explain the basic picture that underlies the almost sure asymptotics of the
total mass U (t) under Assumption (H). Like for the moments, we will give an argument only …