2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158684We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.Published in at http://dx.doi.org/10.1214/07-AIHP115 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)ProbabilityMathematical Physicstext