Related papers: Thermodynamic Formalism for Generalized Countable …

In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(\Sigma_{m_-,m_+}, \sigma_\phi)$ which generalizes the standard bilateral Bernoulli shifts. The space $\Sigma_{m_-,m_+}$…

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$\Gamma$A). This approach contains the important local correlations of DMFT, giving, among…

Measurements of the magnetic Gr\"uneisen parameter ($\Gamma_B$) and specific heat on the Kitaev material candidate $\alpha$-RuCl$_3$ are used to access in-plane field- and temperature-dependence of the entropy up to 12 T and down to 1 K. No…

In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard…

We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that…

Let (\Omega,\mu) be a shift of finite type with a Markov probability, and (Y,\nu) a non-atomic standard measure space. For each symbol i of the symbolic space, let \Phi_i be a measure-preserving automorphism of (Y,\nu). We study skew…

Let $\phi:X\to \mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:X\to X$ over a finite alphabet. Introducing a parameter $\beta>0$ (interpreted as the inverse temperature) we study the regularity of the…

We study $k$-bonacci substitutions. For each we define a renormalization operator associated to it and examine its iterates over potentials in a certain class. We also study the pressure function associated to potentials in this class and…

We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily from a classical result of Parry that the full shift on…

Let $\Omega =\{1,2,\ldots ,d\}^{\mathbb{N}}$, $T$ be the shift acting on $\Omega $, $\mathcal{P}(T)$ the set of $T$-invariant probabilities. Given a H\"{o}lder potential $A$ and a continuous function $F$, we investigate the probabilities…

A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…

The normalized incomplete beta function can be defined either as cumulative distribution function of beta density or as the Gauss hypergeometric function with one of the upper parameters equal to unity. Logarithmic concavity/convexity of…

In the late seventies, Sullivan showed that for a convex cocompact subgroup $\Gamma$ of $\operatorname{SO}^\circ(n,1)$ with critical exponent $\delta>0$, any $\Gamma$-conformal measure on $\partial \mathbb{H}^n$ of dimension $\delta$ is…

We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of the negative entropy, and the biconjugate recovery of the…

We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, $J_A$ and $J_B$, are present, according to the Fibonacci…

In this paper we study correlation measures introduced in \cite{emme_asymptotic_2017}. Denote by $\mu_a(d)$ the asymptotic density of the set $\mathcal{E}_{a,d}=\{n \in \mathbb{N}, \ s_2(n+a)-s_2(n)=d\}$ (where $s_2$ is the sum-of-digits…

The thermodynamics of the 2D XY model is formulated by a transfer matrix method and analyzed by a density matrix renormalization group. The finite-size scaling and the beta function of the model are studied by the Roomany-Wyld…

Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…

It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…

A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,\alpha)\mapsto(X,e^\tau\alpha)$ $(X\in TM,\alpha\in T^*M,\tau\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are…