État actuel et perspectives de l'utilisation des modèles markoviens pour l'étude du comportement des consommateurs
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.
We study excited random walks in i.i.d. random cookie environments in high dimensions, where the th cookie at a site determines the transition probabilities (to the left and right) for the th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that the limiting...
Three-dimensional Laguerre tessellation models became quite popular in many areas of physics and biology. They are generated by locally finite configurations of marked points. Randomness is included by assuming that the set of generators is formed by a marked point process. The present paper focuses on 3D marked Gibbs point processes of generators which enable us to specify the desired geometry of the Laguerre tessellation. In order to prove the existence of a stationary Gibbs measure using a general...