Related papers: Sequence entropy for amenable group actions

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite…

In this paper we introduce the definition of entropy for a partial $\mathbb{Z}$-action. We show that the definition of partial entropy is an extension of the definition of topological entropy for a $\mathbb Z$-action. We also prove that the…

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval),…

In this work, we study the slow entropy type invariant of a dynamical system proposed by A. M. Vershik. We provide an explicit construction of a system whose class of scaling entropy sequences is empty. For this unstable case, we introduce…

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…

Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…

Let $R$ be a ring, let $G$ be an amenable group and let $R\ast G$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function $L$ on the category of left modules over $R$, an additive function on…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…

The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…

In the present paper our main objective is to extend the notion of $D$-sets in countable amenable groups and to discuss its connection with weak mixing for amenable group actions. Further we prove that *-notions are equivalent in the…

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…

We study smooth actions by lattices in higher-rank simple Lie groups. Assuming one element of the action acts with positive topological entropy, we prove a number of new rigidity results. For lattices in $\mathrm{SL}(n,\mathbb{R})$ acting…

Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $(X,\rho)$, it turns out that if the action has positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$ with…

We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups $S$ on discrete abelian groups $A$ by endomorphisms; these extend the classical algebraic entropy for endomorphisms of abelian groups,…

We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups, in which case the invariant is two-valued, with every…

We consider actions of a tileable amenable group $\Gamma$ on a topological space $X$. For a continuous function on $X$, we define the entropy of the number of homologically detectable critical point of the average of that function over…

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…