Coupling, concentration inequalities and stochastic dynamics
نویسندگان
چکیده
We present a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. It is based on concentration inequalities and coupling. We illustrate our approach in a variety of examples for which we obtain several new results with short and non technical proofs. These examples include the symmetric and asymmetric exclusion process and high-temperature spin-flip dynamics (“Glauber dynamic”). We also give a direct proof of the Poincaré inequality, based on coupling, in the context of one-dimensional Gibbs measures. In particular, we cover the case of polynomially decaying potentials, where the log-Sobolev inequality does not hold.
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