On a complex-analytic approach to classifying stationary measures on $S^1$ with respect to the countably supported measures on $PSU(1,1)$

Autor:	Kosenko, Petr
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We provide a complex-analytic approach to the classification of positive stationary measures on $S^1$ with respect to complex finite Borel measures on $PSU(1,1)$ satisfying the finite first moment condition by studying their Poisson-like and Cauchy-like transforms from the perspective of generalized analytic continuation. This approach allows us to establish a functional-analytic criterion for singularity of a hitting measure for random walks on lattices in $PSU(1,1)$. In addition, this approach suggests alternative proofs to the several well-known related results by Furstenberg, Kaimanovich, Guivarc'h-le Jan and Bourgain, among several others. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.11065 Zobrazit plný text záznamu View this record from Arxiv