2019/10/16 by Yuri Kifer, Kifer, Yuri
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1910.07908
openalex publication_date 2019/10/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We consider a ϕ-mixing shift T on a sequence space \Om and study the number \cNN of returns \ TqN(n)\om∈ Aan\ at times qN(n) to a cylinder Aan constructed by a sequence a∈\Om where n runs either until a fixed integer N or until a time τN of the first return \ TqN(n)\om∈ Abm\ to another cylinder Abm constructed by b∈\Om. Here qN(n) are certain functions of n taking on nonnegative integer values when n runs from 0 to N and the dependence on N is the main generalization here which requires certain conditions under which we obtain Poisson distributions limits of \cNN when counting is until N as N→∞ and geometric distributions limits when counting is until τN as N→∞.