Iterates of Volterra operators and indeterminate forms.
Iterations for nonlocal elliptic problems
Convergence of an iteration sequence for some class of nonlocal elliptic problems appearing in mathematical physics is studied.
Iterative solution of quadratic tensor equations for mutual polarisation.
Jordan-Schwinger representations and factorised Yang-Baxter operators.
Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model
Kac’s chaos and Kac’s program
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
Kinetic approach to systems of conservation laws
Kinetic equations with Maxwell boundary conditions
We prove global stability results of DiPerna-Lionsrenormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a boundary inequality condition as it has been established in previous works). We are able to deal with Boltzmann,...
Kinetic formulation for heterogeneous scalar conservation laws
Kinetic methods for Line-energy Ginzburg–Landau models
solutions to the stationary Boltzmann equation in a slab
regularity of velocity averages
La méthode de l’entropie relative pour les limites hydrodynamiques de modèles cinétiques
La scelta delle interazioni inerziali nei continui con microstruttura
Dedicando speciale attenzione all’esempio significativo dei cristalli liquidi di Ericksen [6], viene presentato un apparato assiomatico che consente di dedurre rappresentazioni coerenti delle interazioni d’inerzia e dell’energia cinetica per continui con microstruttura.
Lagrangian and hamiltonian aspects of Josephson type media
Large deviation principles and generalized Sherrington-Kirkpatrick models
Large deviations for partition functions of directed polymers in an IID field
Consider the partition function of a directed polymer in ℤd, d≥1, in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is well known that the free energy of the polymer is equal to a deterministic constant for almost every realization of the field and that the upper tail of the large deviations is exponential. The lower tail of the large deviations is typically lighter than exponential. In this paper we obtain sharp...
Large deviations for the range of an integer valued random walk
Large deviations for voter model occupation times in two dimensions
We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η: ℤ2×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ρ∈(0, 1). In [Probab. Theory Related Fields77 (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log2(t)]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log2(t) when...
Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential