Related papers: Closest Distance between Iterates of Typical Point…

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…

There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on…

We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at…

In this paper, we discuss general criteria of limsup law of iterated logarithm (LIL) for continuous-time Markov processes. We consider minimal assumptions for LILs to hold at zero(at infinity, respectively) in general metric measure spaces.…

We consider the problem of computing expectation values of local functions under the Gibbs distribution of a spin system. In particular, we study two families of linear programming hierarchies for this problem. The first hierarchy imposes…

Consider a linguistic structure formed by $n$ elements, for instance, subject, direct object and verb ($n=3$) or subject, direct object, indirect object and verb ($n=4$). We investigate whether the frequency of the $n!$ possible orders is…

The use of rapidity gaps is proposed as a measure of the spatial pattern of an event. When the event multiplicity is low, the gaps between neighboring particles carry far more information about an event than multiplicity spikes, which may…

For a class of $\zz^2$ Markov Random Fields (MRFs) $\mu$, we show that the sequence of successive differences of entropies of induced MRFs on strips of height $n$ converges exponentially fast (in $n$) to the entropy of $\mu$. These strip…

We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…

The {\em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality, defined as the minimum over all bijections between the point sets of the maximum distance between any pair of points put…

We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…

In this paper, we investigate the asymptotic behavior of the shortest distance between observed orbits in two distinct dynamical systems. Given two measure-preserving transformations $(X, T, \mu)$ and $(X, S, \eta)$ and a Lipschitz…

For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an…

We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prekopa-Leindler type…

We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…

We present a general method to derive continuity estimates for conditional probabilities of general (possibly continuous) spin models sub jected to local transformations. Such systems arise in the study of a stochastic time-evolution of…

In this paper, we give quantitative bounds on the $f$-total variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a sub-geometric rate. These…

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…