Related papers: Entropy and determinants for unitary representatio…
We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a) representation-theoretic characterizations of monomorphisms in all of these categories that…
We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a version of Hofbauer's Markov diagram, (ii) the…
The notion of topological entropy is originally defined for a single action. Later it was extended by Kieffer for arbitrary discrete amenable groups. Recently Friedland defined topological entropy for any discrete group actions amenable or…
We consider the ergodic theory of plane rational maps that preserve the natural holomorphic volume form on the algebraic torus. Specifically we construct natural invariant probability measures for a large class of such maps by intersecting…
A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…
The aim of this paper is to offer an algebraic definition of infinite determinants of finite potent endomorphisms using linear algebra techniques. It generalizes Grothendieck's determinant for finite rank endomorphisms and is equivalent to…
In this paper we introduce for a group $G$ the notion of ultralimit of measure class preserving actions of it, and show that its Furstenberg-Poisson boundaries can be obtained as an ultralimit of actions on itself, when equipped with…
Sofic groups were defined implicitly by Gromov in [Gr99] and explicitly by Weiss in [We00]. All residually finite groups (and hence every linear group) is sofic. The purpose of this paper is to introduce, for every countable sofic group…
We give local upper and lower bounds for the eigenvalues of the modular operator associated to an ergodic action of a compact quantum group on a unital C*-algebra. They involve the modular theory of the quantum group and the growth rate of…
We study in this paper real-valued functions on the space of all sub-$\sigma$-algebras of a probability measure space, and introduce the notion of Kudo-continuity, which is an a priori strengthening of continuity with respect to strong…
Ergodic parameters like the Lyapunov and the conditional exponents are global functions of the invariant measure, but the invariant measure itself contains more information. A more complete characterization of the dynamics by new families…
Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the…
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…
We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic…
In the framework of locally compact quantum groups, we provide an induction procedure for unitary corepresentations as well as coactions on C*-algebras. We prove imprimitivity theorems that unify the existing theorems for actions and…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
For classical dynamical systems, the polynomial entropy serves as a refined invariant of the topological entropy. In the setting of categorical dynamical systems, that is, triangulated categories endowed with an endofunctor, we develop the…