Related papers: Asymptotic shape for subadditve processes on group…

In this article we study asymptotic properties of certain discrete groups $\Gamma$ acting by isometries on a product $\XX=\XX_1\times \XX_2$ of locally compact Hadamard spaces. The motivation comes from the fact that Kac-Moody groups over…

In this work we study the structure of finitely generated groups for which a space of harmonic functions with fixed polynomial growth is finite dimensional. It is conjectured that such groups must be virtually nilpotent (the converse…

Recently, Okounkov, Lazarsfeld and Mustata, and Kaveh and Khovanskii have shown that the growth of a graded linear series on a projective variety over an algebraically closed field is asymptotic to a polynomial. We give a complete…

This paper studies the asymptotic growth and decay properties of solutions of the stochastic pantograph equation with multiplicative noise. We give sufficient conditions on the parameters for solutions to grow at a polynomial rate in $p$-th…

We introduce the notion of dynamic asymptotic dimension growth for actions of discrete groups on compact spaces, and more generally for locally compact \'etale groupoids. Using the work of Bartels, L\"uck, and Reich, we bridge asymptotic…

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results…

We prove a conjecture of Helfgott on the structure of sets of bounded tripling in bounded rank, which states the following. Let $A$ be a finite symmetric subset of $\mathrm{GL}_n(\mathbf{F})$ for any field $\mathbf{F}$ such that $|A^3| \leq…

In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+\alpha}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property…

This paper proves that in a non-elementary relatively hyperbolic group, the logarithm growth rate of any non-elementary subgroup has a linear lower bound by the logarithm of the size of the corresponding generating set. As a consequence,…

In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of…

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for the classifying space for proper actions.…

We discuss the notion of sublinearly bilipschitz equivalences (SBE), which generalize quasi-isometries, allowing some additional terms that behave sublinearly with respect to the distance from the origin. Such maps were originally motivated…

This is a self-contained introduction to the applications of ergodic theory of nonsingular (also known as quasi-invariant) group actions and the structure theorem for finitely generated abelian groups on the extreme values of stationary…

Given a group G acting on a geodesic metric space, we consider a preferred collection of paths of the space -- a path system -- and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the…

Let X be a Hadamard manifold and $\Gamma$ a discrete group of isometries of X which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the geometric limit set of $\Gamma$ in order…

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…

We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…

The solvable Farb growth of a group quantifies how well-approximated the group is by its finite solvable quotients. In this note we present a new characterization of polycyclic groups which are virtually nilpotent. That is, we show that a…