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This paper considers space homogenous Boltzmann kinetic equations in dimension $d$ with Maxwell collisions (and without Grads cut-off). An explicit Markov coupling of the associated conservative (Nanbu) stochastic $N$-particle system is constructed, using plain parallel coupling of isotropic random walks on the sphere of two-body collisional directions. The resulting coupling is almost surely decreasing, and the $L_2$-coupling creation is computed explicitly. Some quasi-contractive and uniform in $N$ coupling / coupling creation inequalities are then proved, relying on $2+alpha$-moments ($alpha >0$) of velocity distributions; upon $N$-uniform propagation of moments of the particle system, it yields a $N$-scalable $alpha$-power law trend to equilibrium. The latter are based on an original sharp inequality, which bounds from above the coupling distance of two centered and normalized random variables $(U,V)$ in $R^d$, with the average square parallelogram area spanned by $(U-U_ast,V-V_ast)$, $(U_ast,V_ast)$ denoting an independent copy. Two counter-examples proving the necessity of the dependance on $>2$-moments and the impossibility of strict contractivity are provided. The paper, (mostly) self-contained, does not require any propagation of chaos property and uses only elementary tools.
We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrodinger equation. By considering the renormalized equation, we extend the quasi-invariance results
It has been shown in the authors companion paper that solutions of Maxwell-Klein-Gordon equations in $mathbb{R}^{3+1}$ possess some form of global strong decay properties with data bounded in some weighted energy space. In this paper, we prove pointw
This paper is devoted to the study of relativistic Vlasov-Maxwell system in three space dimension. For a class of large initial data, we prove the global existence of classical solution with sharp decay estimate. The initial Maxwell field is allowed
We prove global stability results of {sl DiPerna-Lions} renormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions
In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional probabilities in ter