We study the continuous-time limit of a class of Markov chains coming from the evolution of classical open systems undergoing repeated interactions. This repeated interaction model has been initially developed for dissipative quantum systems in Attal and Pautrat (2006) and was recently set up...

We show that the weak infinitesimal generator of a class of Markov processes acts on bounded continuous functions with bounded continuous second derivative as a singular integral with respect to the orthogonality measure of the explicit family of polynomials.