$Riesz \ gases$ form an important class of point processes in statistical physics, consisting in an infinite number of particles interacting through an inverse power-law repulsive pair potential of homogeneity $s$. These objects appear in many unexpected mathematical situations and seem to be sort of universal. An interesting although very challenging question both theoretically and...
Stochastic diffusions are widely used to model physical phenomena, the noise being useful to account for average effects which need not being specified. However, the proposed model is always an approximation that cannot exactly reproduce all the features of the real system (mean, variance, higher order moment...).
Starting from the Gibbs conditioning principle, this talk presents a...
We consider particles whose interaction potential is singular, which is the case of the Coulomb potential. In such a situation, it is more difficult to account for the relative independence of the particles in the limit of their large number, a property known as "molecular chaos". We will see that the modulated energy method provides a fairly robust answer to this question, and we will also...
We derive a formula for the quasi-potential of a one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of the exclusion process with reflecting boundary conditions. In order to observe an evolution of the total mass, the process has to be observed in a longer...
In this presentation, we will introduce and study a Keller-Segel type model describing the time evolution of the spatial distribution of a population of cells subject to three mechanisms.
1) Each cell produces a chemical substance which diffuses in the space and attracts all the other cells (chemotaxis). This corresponds to an attractive and singular mean-field interaction.
2) The cells...
