Related papers: Sofic approximation sequences and sofic mean dimen…
This paper studies groups of maximal size acting harmonically on a finite graph. Our main result states that these maximal graph groups are exactly the finite quotients of the modular group $\Gamma=\left<x,y \ | \ x^2=y^3=1\right>$ of size…
Biconformal gauging of the conformal group has a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dim scale-invariant polynomial actions and a dual action. We solve…
We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known result of Guentner, Willett, and Yu for minimal free actions…
We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…
In this paper we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire's sense) invariant measure has, for each $q>0$, zero lower $q$-generalized fractal dimension.…
The transitivity degree of a group $G$ is the supremum of all integers $k$ such that $G$ admits a faithful $k$-transitive action. Few obstructions are known to impose an upper bound on the transitivity degree for infinite groups. The…
Follow-up comment by the author: Theorem 2.2 in this paper is a special case of Theorems 1.1 and 4.1 in the article "Weighted thermodynamic formalism on subshifts and applications", Asian J. Math. 16 (2012), by J. Barral and D. J. Feng. In…
Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space),…
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…
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 sets of complex rational functions). The dynamics of these…
The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$…
It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Cech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete…
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show…
Let $G$ be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let $N$ be an infinite normal subgroup of $G$, and let $\delta_N$ and $\delta_G$ be the growth rates of $N$ and $G$ with…
In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a…
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…
The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…
We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a…
In this paper, we extend the notion of temporo-spatial differentiation problems to the setting of actions of more general topological groups. The problem can be expressed as follows: Given an action $T$ of an amenable discrete group $G$ on…
We study directional mean dimension of $\mathbb{Z}^k$-actions (where $k$ is a positive integer). On the one hand, we show that there is a $\mathbb{Z}^2$-action whose directional mean dimension (considered as a $[0,+\infty]$-valued function…