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Moderate deviations for random field Curie-Weiss models
Random field Curie-Weiss model disordered mean-field moderate deviations large deviations transfer principle
2012/6/21
The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interes...
Extreme values for two-dimensional discrete Gaussian free field
Extreme values two-dimensional discrete Gaussian free field Probability
2012/6/15
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry...
Asymptotics of the Invariant Measure in Mean Field Models with Jumps
decoupling approximation fluid limit invariant measure McKean-Vlasov equation mean field limit small noise limit
2011/9/16
Abstract: We consider the asymptotics of the invariant measure for the process of the spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects th...
A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics
critical mean-field Swendsen-Wang dynamics Probability
2011/9/9
Abstract: The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the com...
Moderate Deviations for a Curie-Weiss model with dynamical external field
moderate deviations large deviations statistical mechanics Curie-Weiss model dynamic random walks
2011/8/24
Abstract: In the present paper we prove moderate deviations for a Curie-Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard. The re...
Strong-field dipole resonance. I. Limiting analytical cases
population dynamics N-level systems dipolar molecules resonance
2011/3/3
We investigate population dynamics in N-level systems driven beyond the linear regime by a
strong external field, which couples to the system through an operator with nonzero diagonal
elements. 
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
Weak disorder in the stochastic mean-field model of distance II
First passage percolation complete graph extreme value theory hopcount
2010/12/9
In this paper, we study the complete graph Kn with n vertices, where we attach an i.i.d. weight to each of the n(n − 1)/2 edges. We focus on the weight Wn and the number of edges Hn of the minim...
Stochastic Mean-Field Limit: Non-Lipschitz Forces \& Swarming
Mean-field limit diffusion Cucker-Smale collective behavior
2010/12/13
We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the sy...
On Random Field Induced Ordering in the Classical XY Model
Random Field Induced Ordering Classical XY Model
2010/12/13
Consider the classical XY model in a weak random external field pointing along the Y axis with strength . We study the behavior of this model as the range of the interaction is varied.
We prove that...
Optimal coupling for mean field limits
Mean field limits transportation inequalities concentration inequalities optimal coupling
2010/12/9
We review recent quantitative results on the approximation of mean field dif-fusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a l...