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- MICHEL LEDOUX
- 1996

We present a new and simple approach to some of the deviation inequalities for product measures deeply investigated by M. Talagrand in the recent years. Our method is based on functional inequalities of Poincar e and logarithmic Sobolev type and iteration of these inequalities. In particular, we establish with these tools sharp deviation inequalities from… (More)

{ Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontrac-tivity of solutions of Hamilton-Jacobi equations. By the innmum-convolution description of the Hamilton-Jacobi solutions, this approach provides a clear view of… (More)

- M. Ledoux
- 2007

{ We present a direct proof of some recent improved Sobolev inequalities put forward by A. in their wavelet analysis of the space BV (R 2). The argument, relying on pseudo-Poincar e inequalities, allows us to consider several extensions to manifolds and graphs. The classical Sobolev inequality indicates that for every function f on R n vanishing at innnity… (More)

- M. Ledoux
- 2005

In these notes, we survey developments on the asymptotic behavior of the largest eigenvalues of random matrix and random growth models , and describe the corresponding known non-asymptotic exponential bounds. We then discuss some elementary and accessible tools from measure concentration and functional analysis to reach some of these quantitative… (More)

- D. Bakry, T. Coulhon, M. Ledoux
- 1995

We present a simple and direct proof of the equivalence of various functional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or sub-elliptic geometry, as well as on graphs and to certain non-local Sobolev norms. It only uses elementary cutoff arguments. This method has interesting consequences concerning… (More)

- Washburn, S Dingledine, +36 authors J J Kriegstein
- 1998

Differential dependence on GluR2 expression of three characteristic features of AMPA receptors. conditioning enhances short-latency auditory responses of lateral amygdaloid neurons: parallel recordings in the freely behaving rat. and morphological properties of rat basolateral amygdaloid neurons in vitro. recordings from morphologically identified neurons… (More)

- S. G. Bobkov, M. Ledoux
- 1998

where +p is the product measure of the Bernoulli measure with probability of success p, as well as related inequalities, which may be shown to imply in the limit the classical Gaussian logarithmic Sobolev inequality as well as a logarithmic Sobolev inequality for Poisson measure. We further investigate modified logarithmic Sobolev inequalities to analyze… (More)

- M. Ledoux
- 1999

| We analyze recent proofs of decay of correlations and logarithmic Sobolev inequalities for unbounded spin systems in the perturbative regime developed by B. Zegarlinski, B. Heller, Th. Bodineau, N. Yoshida. We investigate to this task a simple analytic model together with a new L 1 bound on the correlations. Proofs are short and self-contained. Let be a… (More)

- M. Ledoux
- 2004

– We survey recent works on the connection between spectral gap and logarithmic Sobolev constants, and exponential integrability of Lipschitz functions. In particular, tools from measure concentration are used to describe bounds on the diameter of a (compact) Riemannian manifold and of Markov chains in terms of the first eigenvalue of the Lapla-cian and the… (More)

- Cécile Ané, ·Michel Ledoux, C. Ané, M. Ledoux
- 1998

We establish modified logarithmic Sobolev inequalities for the path distributions of some continuous time random walks on graphs, including the simple examples of the discrete cube and the lattice ZZ d. Our approach is based on the Malliavin calculus on Poisson spaces developed by J. Picard and stochastic calculus. The inequalities we prove are well adapted… (More)