Hausdorff dimension of the SLE curve intersected with the real line.
Heat kernel asymptotics on the lamplighter group.
Heisenberg's picture and non commutative geometry of the semi classical limit in quantum mechanics
Heterogeneous queueing systems with balking
Hierarchical pinning model in correlated random environment
We consider the hierarchical disordered pinning model studied in (J. Statist. Phys.66 (1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (Probab. Theory Related Fields148 (2010) 159–175,...
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
Homogenization results for a linear dynamics in random Glauber type environment
We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green–Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.
Huge random structures and mean field models for spin glasses.
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst.
Hydrodynamic limit for a particle system with degenerate rates
We study the hydrodynamic limit for some conservative particle systems with degenerate rates, namely with nearest neighbor exchange rates which vanish for certain configurations. These models belong to the class of kinetically constrained lattice gases (KCLG) which have been introduced and intensively studied in physical literature as simple models for the liquid/glass transition. Due to the degeneracy of rates there exist blocked configurations which do not evolve under the dynamics and in general...
Hydrodynamic limit for asymmetric mean zero exclusion processes with speed change
Hydrodynamic limit for perturbation of a hyperbolic equilibrium point in two-component systems
Hydrodynamic limit of a d-dimensional exclusion process with conductances
Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m aj αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d ∂xk ∂Wk Φ(ρ). We also derive some properties of the operator ∑k=1d ...
Hydrodynamic limit of mean zero asymmetric zero range processes in infinite volume
Hydrodynamic limit of zero range processes among random conductances on the supercritical percolation cluster.
Hydrodynamic scaling limit of continuum solid-on-solid model.
Hydrodynamical behavior of symmetric exclusion with slow bonds
We consider the exclusion process in the one-dimensional discrete torus with points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance , with . We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter . If , the hydrodynamic limit is given by the usual heat equation. If , it is given by a parabolic equation involving an operator , where ...
Hydrodynamical limit for asymmetric attractive particle systems on
Hydrodynamical limit for the asymmetric zero-range process
Hypercontractivité et isopérimétrie gaussienne. Applications aux systèmes de spins