Abstract: Laguerre processes are particular diffusions on the half-line whose invariant measures are the Gamma distributions. In this talk, we will present discrete analogues under the form of birth and death processes whose invariant measures are the negative binomial distributions. The analogy will be strengthened into intertwinings, which is are commutation relations between the corresponding Markov semi-groups enabling convenient transfers between the continuous and discrete frameworks. In particular, we will be interested into the estimates of ergodic coefficients measuring the speed of convergence to equilibrium, such as the spectral gap or the (modified) logarithmic Sobolev constant.

Work in collaboration with Pierre Patie.