In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of graphons. …

In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of mass, …

In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions’ evolution. We explore the natural question of the large population limit with two …

In this paper we are interested in the large time behavior of linear kinetic equations with heavy-tailed local equilibria. Our main contribution concerns the kinetic Lévy-Fokker- Planck equation, for which we adapt hypocoercivity techniques in order …

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The …

We go back to the question of the regularity of the velocity average ${\int f(x,v)\psi(v) d \mu( v)}$when $f$ and $v\cdot \nabla\_xf$ both belong to $L^2$, and the variable $v$ lies in a discrete subset of $\mathbb R^D$. First of all, we provide a …

In this note, we investigate some questions around velocity averaging lemmas, a class of results which ensure the regularity of the velocity average ${\int f(x,v)\psi(v) d \mu( v)}$ when $v\cdot \nabla\_xf$ both belong to $L^p$, $p \in \[1, \infty)$ …

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The …

The work of this thesis belongs to the field of partial differential equations. More specifically, it is linked to the problematic of scale changes in the context of kinetic of gas. Indeed, knowing that there exists different scales of description for a gas (microscopic, mesoscopic and macroscopic scale), we want to link these different associated scales in a context where some randomness acts, in initial data and/or distributed on all the time interval.

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