Growth of the asymptotic dimension function for groups

Asymptotic aspects of Schreier graphs and Hanoi Towers groups

We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of examples, called Hanoi Towers groups since they model the well known Hanoi Towers Problem, that illustrate some of the possible types of behavior.

多项式增长群上次可加过程的渐近形状

Asymptotic shape for subadditve processes on groups of polynomial growth

本研究探讨了虚拟幂零群上次可加过程的极限形状定理，在代数结构框架内提出了该定理的广义形式，扩展了次可加遍历理论以涵盖至多和至少线性随机增长过程，并给出了应用与示例。

Decomposition complexity growth of finitely generated groups

Finite decomposition complexity and asymptotic dimension growth are two generalizations of M. Gromov's asymptotic dimension which can be used to prove property A for large classes of finitely generated groups of infinite asymptotic dimension. In this paper, we introduce the notion of decomposition complexity growth, which is a quasi-isometry invariant generalizing both finite decomposition complexity and dimension growth. We show that subexponential decomposition complexity growth implies property A, and is preserved by certain group and metric constructions.

群作用与群胚的动态渐近维数增长

Dynamic asymptotic dimension growth for group actions and groupoids

该研究引入离散群作用及局部紧平展群胚的动态渐近维数增长概念，证明其与有界几何离散度量空间的渐近维数增长等价，推导相关群胚的可和性结论，并将其应用于证明带系数Baum-Connes猜想成立。

Growth of permutational extensions

We study the geometry of a class of group extensions, containing permutational wreath products, which we call "permutational extensions". We construct for all natural number k a torsion group with growth function asymptotically $\exp(n^{1-(1-α)^k}),\quad 2^{3-3/α}+2^{2-2/α}+2^{1-1/α}=2$, and a torsion-free group with growth function asymptotically $\exp(\log(n)n^{1-(1-α)^k})$. These are the first examples of groups of intermediate growth for which the growth function is known. We construct a group of intermediate growth that contains the group of finitely supported permutations of a countable …

virtually abelian 群的扭曲共轭增长

The twisted conjugacy growth of virtually abelian groups

本文研究了 virtually abelian 群上与扭曲共轭相关的多个增长函数的渐近性，并证明这些增长函数均表现出多项式渐近行为。

Drift and entropy growth for random walks on groups

In this paper we consider finitary symmetric random walks on groups. We construct new possible asymptotics for the drift. We show that the drift can be very close to linear ant yet sublinear. We also give estimates for entropy growth of these random walks. In particular, we prove that there exist infinitely many asymptotics of entropy.

On the growth of algebras, semigroups, and hereditary languages

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.

同步点：增长、渐进行为、同余关系以及同步ζ函数

Synchronization points: growth, asymptotics, congruences, and the synchronization zeta function

本文研究了同步点的增长、渐进行为及同余关系，引入同步ζ函数并探讨其与拓扑熵和Reidemeister束缚的联系。

On Commensurizer Growth

We study new asymptotic invariant of a pair consisting of a group and a subgroup, which we call Commensurizer Growth. We compute the commensurizer growth for several examples, concentrating mainly on the case of a locally compact topological group and a lattice inside it.

Reidemeister 和 Nielsen 数：增长速率、渐进行为、动力学ζ函数和高斯同余

The Reidemeister and the Nielsen numbers: growth rate, asymptotic behavior, dynamical zeta functions and the Gauss congruences

本文从动力学角度研究Reidemeister和Nielsen数序列的增长速率、渐进行为及高斯同余，证明了相关ζ函数的有理性和序列的生长特性。