Offers an introduction to large deviations. This book is divided into two parts: theory and
applications. It presents basic large deviation theorems for iid sequences, Markov …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

We consider nonlinear parabolic SPDEs of the form \partial_tu=\calLu+σ(u)̇w, where ̇w
denotes space-time white noise, σ:R→R is globally Lipschitz continuous, and \calL is the …

Polymer chains that interact with themselves and/or with their environment are fascinating
objects, displaying a range of interesting physical and chemical phenomena. The focus in …

We define the Anderson hamiltonian on the two dimensional torus $\mathbb R^ 2/\mathbb
Z^ 2$. This operator is formally defined as $\mathscr H:=-\Delta+\xi $ where $\Delta $ is the …

We consider the parabolic Anderson problem∂ tu= Δ u+ ξ (x) u on ℝ+× ℤ d with localized
initial condition u (0, x)= δ 0 (x) and random iid potential ξ. Under the assumption that the …

We consider the stochastic heat equation of the following form:\begin {equation*}\frac
{\partial}{\partial t} u_t (x)=(\mathcal {L} u_t)(x)+ b (u_t (x))+\sigma (u_t (x))\dot {F} _t …

We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem
for the heat equation with random potential on Z^ d. We consider general iid potentials and …

We study a random walk pinning model, where conditioned on a simple random walk Y on
Zd acting as a random medium, the path measure of a second independent simple random …

The parabolic Anderson problem is the Cauchy problem for the heat equation∂ tu (t, z)= Δ u
(t, z)+ ξ (z) u (t, z) on (0,∞)× ℤ d with random potential (ξ (z): z∈ ℤ d). We consider …