Abstract: In this talk, we will examine quantitative recurrence in dynamical systems. Our aim is to describe how the law of return times to natural small targets evolves as they get smaller and to identify the corresponding limit behaviors. We will focus in particular on Countable Markov Shifts (CMS), a paradigmatic class of dynamical systems that generalizes both subshifts of finite type and Markov chains on countable state spaces. In the positive recurrent case, CMS exhibit a known well-known dichotomy, with the Poisson point process arising as the main limit. Our main interest, however, lies in the null recurrent case, where the Fractional Poisson process plays a central role. We will also show that, for natural targets, other limiting processes may appear in this setting.
Returns to rare events for countable Markov shifts
11.12.2025 15:15 - 18:00
Organiser:
H. Bruin, R. Zweimüller
Location: