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 in equalities… (More)

We present a simple proof, based on modi ed logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure… (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… (More)

– 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… (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… (More)

– We use the continuity theorem of T. Lyons for rough paths in the p-variation topology to produce an elementary approach to the large deviation principle and the support theorem for diffusion… (More)

3 These notes form a summary of a mini-course given at the Eidgenn ossische Technis-che Hochschule in Z urich in November 1998. They aim to present some of the basic ideas in the geometric… (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 Z… (More)