Economic system dynamics.
Einstein relation for biased random walk on Galton–Watson trees
We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton–Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrarily slow traps.
Elementary potential theory on the hypercube.
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular...
Entropy flux far from equilibrium in solids and in non viscous gases
One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some...
Entropy maximisation problem for quantum relativistic particles
The entropy of an ideal gas, both in the case of classical and quantum particles, is maximised when the number particle density, linear momentum and energy are fixed. The dispersion law energy to momentum is chosen as linear or quadratic, corresponding to non-relativistic or relativistic behaviour.
Entropy of random walk range
We study the entropy of the set traced by an n-step simple symmetric random walk on ℤd. We show that for d≥3, the entropy is of order n. For d=2, the entropy is of order n/log2n. These values are essentially governed by the size of the boundary of the trace.
Équation de transport. Théorie spectrale et approximation de la diffusion
Équations de moment et conditions d'entropie pour des modèles cinétiques
Equilibrium fluctuations for a one-dimensional interface in the solid on solid approximation.
Equilibrium fluctuations for lattice gases
Equilibrium states for the Landau-Fermi-Dirac equation
A kinetic collision operator of Landau type for Fermi-Dirac particles is considered. Equilibrium states are rigorously determined under minimal assumptions on the distribution function of the particles. The particular structure of the considered operator (strong non-linearity and degeneracy) requires a special investigation compared to the classical Boltzmann or Landau operator.
Erdős-Renyi random graphs forest fires self-organized criticality.
Ergodic behaviour of “signed voter models”
We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat.41(2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site and a site is negative (respectively positive) the site will contribute towards the flip rate of if and only if the two current spin values are equal (respectively opposed)....
Ergodicity of PCA: equivalence between spatial and temporal mixing conditions.
Erratum to Numer. Math. 52, 219-240 (1988). Product Integration for the Linear Transport Equation in Slab Geometry.
Error analysis for the finite element approximation of a radiative transfer model
Estimate of spectral gap for continuous gas
Euler hydrodynamics for attractive particle systems in random environment
We prove quenched hydrodynamic limit under hyperbolic time scaling for bounded attractive particle systems on in random ergodic environment. Our result is a strong law of large numbers, that we illustrate with various examples.