Derrida's generalised random energy models 1 : models with finitely many hierarchies
Derrida's generalized random energy models 2 : models with continuous hierarchies
Développement asymptotique de la densité d'états pour des opérateurs de Schrödinger aléatoires singuliers
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
Disorder relevance at marginality and critical point shift
Recently the renormalization group predictions on the effect of disorder on pinning models have been put on mathematical grounds. The picture is particularly complete if the disorder is relevant or irrelevant in the Harris criterion sense: the question addressed is whether quenched disorder leads to a critical behavior which is different from the one observed in the pure, i.e. annealed, system. The Harris criterion prediction is based on the sign of the specific heat exponent of the pure system,...
Disorder relevance for the random walk pinning model in dimension 3
We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk (Ys)s≥0 on ℤd with jump rate ρ > 0, which plays the role of disorder, the law up to time t of a second independent random walk (Xs)0≤s≤t with jump rate 1 is Gibbs transformed with weight eβLt(X,Y), where Lt(X, Y) is the collision local time between X and Y up to time t. As the inverse temperature β varies, the model undergoes a localization–delocalization transition at...