Related papers: Naive mean dimension
We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
We investigate bounds on the dimension of cohomology groups for finite groups acting on an irreducible kG-module for G a finite group of bound sectional p-rank and k an algebraically closed field of characteristic p.
We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height growth and height counting problems in random orbits.
We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must…
We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the asymptotic dimension of any of its box spaces is bounded…
We extend the notion of representability dimension to partial actions and introduce a notion of dual representability dimension for global actions by finite abelian groups. We show that the Rokhlin dimension of a partial action by a finite…
We show that the harmonic measure on a product of boundaries satisfies dimension conservation for a random walk with non-elementary marginals on a countable group acting on a product of hyperbolic spaces under the finite first moment…
I give a construction of compact group action on a finite dimensional space Y, whose orbit space is infinite dimensional.
In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups of rational maps.
Let (X,Z) be a dynamical system on a compact metric X and let X be the countable union of closed invariant subsets X_i, i in N. We prove that mdim X =sup {mdim X_i : i in N}.
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…
We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in…
Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
We prove that the upper metric mean dimension of $C^0$-generic homeomorphisms, acting on a compact smooth boundaryless manifold with dimension greater than one, coincides with the dimension of the manifold. In the case of continuous…
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…
We define sofic, weakly sofic, linear sofic and hyperlinear metric groups and discuss some issues involving axiomatizability of these classes in continuous logic.
We introduce the concept of Rokhlin dimension for actions of residually compact groups on C*-algebras, which extends and unifies previous notions for actions of compact groups, residually finite groups and the reals. We then demonstrate…
We study how analytic functions, and more generally quasiregular mappings, distort Nagata dimension. Quasiconformal mappings of domains preserve the Nagata dimension of compact subsets, in view of a result of Lang and Schlichenmaier. We…