17 citations · 71 across the 34 of their papers we have counts for
34 papers
Commensurating actions and self-similar groups
Nicolás Matte Bon, Volodymyr Nekrashevych, Tianyi Zheng
Commensurating actions govern how a group can act on non-positively curved cube complexes. We obtain a complete picture of them for a class of finitely generated groups acting on r…
Concentration inequalities for maximal displacement of random walks on groups of polynomial growth
Jérémie Brieussel, Romain Tessera, Tianyi Zheng
We prove Gaussian concentration inequalities for maximal displacement of compactly supported random walks on a compactly generated locally compact group with polynomial growth. Con…
Infinite stationary measures of co-compact group actions
Mohammedsaid Alhalimi, Tom Hutchcroft, Minghao Pan +2
Let be a finitely generated group, and let be a nondegenerate, finitely supported probability measure on . We show that every co-compact action on a locally compact…
Confined subgroups in groups with contracting elements
Inhyeok Choi, Ilya Gekhtman, Wenyuan Yang +1
In this paper, we study the growth of confined subgroups through boundary actions of groups with contracting elements. We establish that the growth rate of a confined subgroup is s…
Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition
Zhiqiang Li, Tianyi Zheng
In the second paper [LZ24b] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the -sphere called expanding Thursto…
Four infinite families of chiral -polytopes of type with solvable automorphism groups
Dong-Dong Hou, Tian-Tian Zheng, Rui-Rui Guo
We construct four infinite families of chiral -polytopes of type , with , , and automorphisms for every positive integer , res…
Furstenberg entropy spectra of stationary actions of semisimple Lie groups
Jérémie Brieussel, Tianyi Zheng
We determine Furstenberg entropy spectra of ergodic stationary actions of and its lattices. The constraints on entropy spectra are derived from a refinement of t…
Liouville property for groups and conformal dimension
Nicolás Matte Bon, Volodymyr Nekrashevych, Tianyi Zheng
Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the study of self-similar spaces, such as spaces with an expanding self-covering (e.g. Julia…
Limit theorems for some long range random walks on torsion free nilpotent groups
Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste +2
We consider a natural class of long range random walks on torsion free nilpotent groups and develop limit theorems for these walks. Given the original discrete group and a rand…
Growth of groups with linear Schreier graphs
Laurent Bartholdi, Volodymyr Nekrashevych, Tianyi Zheng
We introduce a new method of proving upper estimates of growth of finitely generated groups and constructing groups of intermediate growth using graphs of their actions. These esti…
Law of large numbers for the drift of two-dimensional wreath product
Anna Erschler, Tianyi Zheng
We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite -moment. This…
Isoperimetric profiles and random walks on some groups defined by piecewise actions
Laurent Saloff-Coste-Costeb, Tianyi Zheng
We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple {\em gluing} of such. I…
On FC-central extensions of groups of intermediate growth
Tianyi Zheng
It is shown that FC-central extensions retain sub-exponential volume growth. A large collection of FC-central extensions of the first Grigorchuk group is provided by the constructi…
Neretin groups admit no non-trivial invariant random subgroups
Tianyi Zheng
We show that Neretin groups have no non-trivial invariant random subgroups. These groups provide first examples of non-discrete, compactly generated, locally compact groups with th…
On the spectrum of asymptotic entropies of random walks
Omer Tamuz, Tianyi Zheng
Given a random walk on a free group, we study the random walks it induces on the group's quotients. We show that the spectrum of asymptotic entropies of the induced random walks ha…
On rigid stabilizers and invariant random subgroups of groups of homeomorphisms
Tianyi Zheng
A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an appl…
Long range random walks and associated geometries on groups of polynomial growth
Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste +2
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to…
Prime orbit theorems for expanding Thurston maps
Zhiqiang Li, Tianyi Zheng
We obtain an analogue of the prime number theorem for a class of branched covering maps on the -sphere called expanding Thurston maps , which are topological models of some r…
Growth of periodic Grigorchuk groups
Anna Erschler, Tianyi Zheng
On torsion Grigorchuk groups we construct random walks of finite entropy and power-law tail decay with non-trivial Poisson boundary. Such random walks provide near optimal volume l…
Isoperimetric inequalities, shapes of Følner sets and groups with Shalom's property
Anna Erschler, Tianyi Zheng
We prove an isoperimetric inequality for groups. As an application, we obtain lower bound on Følner functions in various nilpotent-by-cyclic groups. Under a regularity assumption,…
Shalom's property and extensions by of locally finite groups
Jérémie Brieussel, Tianyi Zheng
We show that every finitely generated extension by of a locally normally finite group has Shalom's property . This is no longer true without the norma…
Random walks among time increasing conductances: heat kernel estimates
Amir Dembo, Ruojun Huang, Tianyi Zheng
For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequal…
Occupation measure of random walks and wired spanning forests in balls of Cayley graphs
Russell Lyons, Yuval Peres, Xin Sun +1
We show that for finite-range, symmetric random walks on general transient Cayley graphs, the expected occupation time of any given ball of radius is .. We also stu…
Random walks on the discrete affine group
Jérémie Brieussel, Ryokichi Tanaka, Tianyi Zheng
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of…