Related papers: The Lanford-Ruelle theorem for actions of sofic gr…

We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow…

We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…

We show that the class of sofic actions is closed under direct products and contains a (non-unique) maximal element in the weak containment order. For any sofic group we construct nice sofic approximations such that all the sofic actions…

The main aim of the present set of notes is to give new, short and essentially self-contained proofs of some classical, as well as more recent, results about random walks on groups. For instance, we shall see that the drift characterization…

In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a…

The group of homeomorphisms of the closed interval that are absolutely continuous and have an absolutely continuous inverse was shown by Solecki to admit a natural Polish group topology $\tau_{ac}$. We show that, under mild conditions on a…

We consider the dynamical system given by a diagonalizable element $a$ of a closed linear unimodular algebraic subgroup $G$ of the special linear group over the $p$-adic numbers acting by translation on a finite volume quotient $X$.…

In this paper, we introduce the notions of neutralized packing pressures and neutralized measure-theoretic pressures on subsets for a finitely generated free semigroup action. Let $X$ be a compact metric space and $\mathcal{G}$ be a finite…

We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…

Let $G$ be a group and $\phi:H\to G$ be a contracting homomorphism from a subgroup $H<G$ of finite index. V.Nekrashevych [25] associated with the pair $(G,\phi)$ the limit dynamical system $(\lims,\si)$ and the limit $G$-space $\limGs$…

Let $\Gamma$ be a countably infinite group. A common theme in ergodic theory is to start with a probability measure-preserving (p.m.p.) action $\Gamma \curvearrowright (X, \mu)$ and a map $f \in L^1(X, \mu)$, and to compare the global…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

We focus on a sequence of functions $\{f_n\}$, defined on a compact manifold with boundary $S$, converging in the $C^k$ metric to a limit $f$. A common assumption implicitly made in the empirical sciences is that when such functions…

The Hammersley-Clifford theorem states that if the support of a Markov random field has a safe symbol then it is a Gibbs state with some nearest neighbour interaction. In this paper we generalise the theorem with an added condition that the…

We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…

Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and {\Gamma} be an arithmetic lattice. One can associate a probability measure {\mu}(H) on {\Gamma}\G for each…

Let $a_n$ be the random increasing sequence of natural numbers which takes each value independently with decreasing probability of order $n^{-\alpha}$, $0 < \alpha < 1/2$. We prove that, almost surely, for every measure-preserving system…

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically…

This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…

We prove that if a Borel probability measure (\mu) on (\T) is invariant under the action of a "large" multiplicative semigroup (lower logarithmic density is positive) and the action of the whole semigroup is ergodic then (\mu) is either…