Heat kernel asymptotics on the lamplighter group.
Huge random structures and mean field models for spin glasses.
La matematica nel processo di cristallizzazione di polimeri: modelli stocastici e deterministici
Lévy Processes, Saltatory Foraging, and Superdiffusion
It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...
Localisation for the spin J-boson hamiltonian
Marches pseudo-aléatoires issues de substitutions : aspects statistiques
Mean Green's function of the Anderson model at weak disorder with an infra-red cut-off
Méthodes de noyaux et de symboles en calcul stochastique non commutatif
On a probabilistic description of small scale structures in 3D fluids
On a stochastic model of a cascade
On small solutions of second order differential equations with random coefficients
We consider the equation where is a given increasing sequence of positive numbers, and is chosen at random so that are totally independent random variables uniformly distributed on interval . We determine the probability of the event that all solutions of the equation tend to zero as .
On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.
On the multiple overlap function of the SK model.
In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1i ... σsi. These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.
On the proof of the Parisi formula by Guerra and Talagrand
The Parisi formula is an expression for the limiting free energy of the Sherrington-Kirkpatrick spin glass model, which had first been derived by Parisi using a non-rigorous replica method together with an hierarchical ansatz for the solution of the variational problem. It had become quickly clear that behind the solution, if correct, lies an interesting mathematical structure. The formula has recently been proved by Michel Talagrand based partly on earlier ideas and results by Francesco Guerra....
On the smallest eigenvalue of the Stokes operator in a domain with fine-grained random boundary.
On the vector process obtained by iterated integration of the telegraph signal.
Post-gelation behavior of a spatial coagulation model.
Probability and quanta: why back to Nelson?
We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.
Problemi di geometria stocastica nei processi di cristallizzazione di polimeri. Aspetti modellistici, statistici e computazionali
Projections de mouvements browniens régularisés via l'action d'un groupe de Lie hilbertien