Related papers: Harmonicity of Gibbs measures
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any moment condition on the measure. We also extend our method to…
Given a finitely generated group, the well-known Stability Problem asks whether the non-triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non-constant bounded harmonic functions) depends on the choice…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…
We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…
We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\V$ of functions of finite variation…
The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In…
We find uniform lower bounds on the drift for a large family of random walks on graph products, of the form $ \mathbb{P} (|Z_{n}| \leq \kappa n) \leq e ^{-\kappa n} $ for $ \kappa > 0 $. This includes the simple random walk for a…
We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\mu$ such that, for…
We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent case described in Stufler (2018, Random Structures \&…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.
Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces.…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
Tolerance intervals provide bounds that contain a specified proportion of a population with a given confidence level, yet their construction remains challenging when parametric assumptions fail or sample sizes are small. Traditional…
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…