Domination criterion for some positive operators and quasi-stationary distributions.

Resumen:   After a short introduction to the concept of quasi-stationary distributions, I will present the typical and well known “finite state space” convergence results. In a second time, I will present domination criteria for the quasi-compactness of positive operators and show some applications of these spectral theoretical results for the study of quasi-stationary distributions. The talk will conclude with an illustration on the interplay between these results and recent ones on weighted branching processes, obtained in collaboration with Nicolas Zalduendo.