arXiv subjects
Publications and source records attributed to Baptiste Nicolas Huguet.
We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensional case, this constant is even optimal. From these inequalities, we derive concentration results, which allow concluding the case of the pathological dimension two.
We study a mutliscale jump process introduced in a work by Crudu, Debussche, Muller and Radulescu. Using an adequate coupling, we are able to prove the strong convergence, for the uniform topology, to a piecewise deterministic Markov process. Under some additional regularity, we also obtain a central limit theorem and prove that the fluctuations of the continuous scale converge, in a weaker sense, to the solution of a stochastic differential equation.
We obtain new sharp weighted Poincar{é} inequalities on Riemannian manifolds for a general class of measures. When specialised to generalised Cauchy measures, this gives a unified and simple proof of the weighted Poincar{é} inequality for the whole range of parameters, with the optimal spectral gap, the error term and the extremal functions.