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Publications Influence

Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré

- D. Bakry, P. Cattiaux, A. Guillin
- Mathematics
- 12 March 2007

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one… Expand

196 15- PDF

Quasi-stationary distributions and diffusion models in population dynamics

- P. Cattiaux, P. Collet, A. Lambert, S. Martínez, S. M'el'eard, J. Martín
- Mathematics
- 27 March 2007

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an… Expand

114 14- PDF

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry

- F. Barthe, P. Cattiaux, Cremonini Roberto
- Mathematics
- 13 July 2004

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide… Expand

133 13- PDF

A simple proof of the Poincaré inequality for a large class of probability measures

- D. Bakry, F. Barthe, P. Cattiaux, A. Guillin
- Mathematics
- 2 April 2008

Abstract. We give a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures on… Expand

157 12- PDF

Probabilistic approach for granular media equations in the non-uniformly convex case

- P. Cattiaux, A. Guillin, F. Malrieu
- Mathematics
- 22 March 2006

We use here a particle system to prove both a convergence result (with convergence rate) and a deviation inequality for solutions of granular media equation when the confinement potential and the… Expand

103 11- PDF

Competitive or weak cooperative stochastic Lotka–Volterra systems conditioned on non-extinction

- P. Cattiaux, S. Méléard
- Mathematics, Medicine
- Journal of mathematical biology
- 3 November 2008

We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two… Expand

56 9- PDF

Hypoelliptic non-homogeneous diffusions

- P. Cattiaux, Laurent Mesnager
- Mathematics
- 1 August 2002

Abstract. Let be a time dependent second order operator, written in usual or Hörmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process,… Expand

41 8

DEVIATION BOUNDS FOR ADDITIVE FUNCTIONALS OF MARKOV PROCESSES

- P. Cattiaux, A. Guillin
- Mathematics
- 1 March 2006

In this paper we derive non asymptotic deviation bounds for P� � � � 1 Z t 0 V (X s)ds Z V dµ � � � R � where X is a µ stationary and ergodic Markov process and V is some µ integrable function. These… Expand

56 7- PDF

On quadratic transportation cost inequalities

- P. Cattiaux, A. Guillin
- Mathematics
- 1 October 2006

Abstract In this paper we study quadratic transportation cost inequalities. To this end we introduce new families of inequalities (for quadratic transportation cost and for relative entropy) that are… Expand

54 6- PDF

Large deviations and Nelson processes

- P. Cattiaux, Christian Léonard
- Mathematics
- 1995

We obtain a large deviation principle for the empirical process of a large dynamical stochastic System of non-interacting particles. A careful study of the rate function of this large deviation… Expand

35 5