Développement asymptotique de la densité d'états pour des opérateurs de Schrödinger aléatoires singuliers
Dichotomy in a scaling limit under Wiener measure with density.
Die Polynome von Yang-Lee und ihre Nullstellen.
Different approaches to stochastic parabolic differential equations
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
Diffuse-interface treatment of the anisotropic mean-curvature flow
We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.
Diffusion and scattering of shocks in the partially asymmetric simple exclusion process.
Diffusion approximation of nonlinear electron phonon collision mechanisms
Diffusion limit of the Lorentz model : asymptotic preserving schemes
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...
Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...
Diffusion limits for the initial-boundary value problem of the Goldstein--Taylor model.
Diffusive long-time behavior of Kawasaki dynamics.
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs and areequivalentif the Newton polygons of the corresponding partition functions...
Directed animals and gas models revisited.
Directed polymer in random environment and last passage percolation*
The sequence of random probability measures νn that gives a path of length n, times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
Disclinations and hedgehogs in nematic liquid crystals with variable degree of orientation
There is enough evidence to re-examine disclinations and hedgehogs, the singularities often observed in nematic liquid crystals, in the light of a new theory that allows for local changes in the degree of orientation.
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
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...
Dissipation effects in the ratchetlike Fermi acceleration.