Related papers: Equilibrium states beyond specification and the Bo…

We give an equivalent condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [6] and…

In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…

We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…

We study equilibrium states of an infinite system of interacting particles in a Euclidean space. The particles bear `unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits…

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to…

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…

For strongly dissipative H\'enon maps at the first bifurcation where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e., prove the existence and…

We show that, for a robust ($C^2$-open) class of random non-uniformly expanding maps, there exists equilibrium states for a large class of potentials.In particular, these sytems have measures of maximal entropy. These results also give a…

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

We study Markov decision problems where the agent does not know the transition probability function mapping current states and actions to future states. The agent has a prior belief over a set of possible transition functions and updates…

We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…

There are several known constructions of equilibrium states for H\"older continuous potentials in the context of both subshifts of finite type and uniformly hyperbolic systems. In this article we present another method of building such…

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is…

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…

In this note, we establish an original result for the thermodynamic formalism in the context of expanding circle transformations with an indifferent fixed point. For an observable whose continuity modulus is linked to the dynamics near such…

Let $f:I \to I$ be a $C^2$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto -t\log|Df(x)|$ for $t$…

Given a finite irreducible set of real $d \times d$ matrices $A_1,\ldots,A_M$ and a real parameter $s>0$, there exists a unique shift-invariant equilibrium state associated to $(A_1,\ldots,A_M,s)$. In this article we characterise the…

Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode…

In this paper we solve two open problems in ergodic theory. We prove first that if a Doeblin function $g$ (a $g$-function) satisfies \[\limsup_{n\to\infty}\frac{\mbox{var}_n \log g}{n^{-1/2}} < 2,\] then we have a unique Doeblin measure…