Asymptotic behaviors of random walks on countable groups Page 1 Asymptotic behaviors of
random walks on countable groups Tianyi Zheng (郑天一) Abstract In this note we survey some …

Research in recent years has highlighted the deep connections between the algebraic,
geometric, and analytic structures of a discrete group. New methods and ideas have …

We prove that a supercritical branching random walk on a transient Markov chain converges
almost surely under rescaling to a random measure on the Martin boundary of the …

Positive harmonic functions on groups and covering spaces - ScienceDirect Skip to main
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We study the isoperimetric and spectral profiles of certain families of finitely generated
groups defined via actions on labelled Schreier graphs and simple gluing of such. In one of …

1. Introduction A smooth family of Riemannian metrics. gt//t2Œ0; T/is a Ricci flow if it satisfies
the equation@ t gt/D 2 Ric gt/for every t 2 Œ0; T/, where Ric. gt//denotes the Ricci tensor of …

Lyons and Sullivan conjectured in Lyons and Sullivan (J. Differential Geom. 19 (2), 299–
323,) that if p: M→ N is a normal Riemannian covering, with N closed, and M has …

arXiv:1906.11723v2 [math.DG] 28 Nov 2019 Positive harmonic functions on covering spaces
Page 1 arXiv:1906.11723v2 [math.DG] 28 Nov 2019 Positive harmonic functions on covering …

Polynomially growing harmonic functions on connected groups Page 1 Groups Geom. Dyn. 17
(2023), 111–126 DOI 10.4171/GGD/660 © 2022 European Mathematical Society Published by …

For a Riemannian covering p: M2→ M1, we compare the spectrum of an essentially self-
adjoint differential operator D1 on a bundle E1→ M1 with the spectrum of its lift D2 on p∗ …