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{ 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)
{ 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)
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)
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)
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)
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)