Related papers: Countable Markov shifts with exponential mixing

Capacity is an important quantity in potential theory and in the study of Markov processes. We give equivalent conditions between the capacity, the mean exit time, and the Green function for non-reversible diffusions.

We prove exponential decay of correlations for a class of $C^{1+\alpha}$ uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open…

We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to…

We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather natural condition.

This paper studies the entropy of tree-shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree-shift of finite type is equivalent to solving a system of nonlinear recurrence equations.…

The "carries" when n random numbers are added base b form a Markov chain with an "amazing" transition matrix determined by Holte. This same Markov chain occurs in following the number of descents or rising sequences when n cards are…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

We prove a functional limit theorem for Markov chains that, in each step, move up or down by a possibly state dependent constant with probability $1/2$, respectively. The theorem entails that the law of every one-dimensional regular…

For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological…

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use…

A simple model of the new notion of "Markov up" processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions.

We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…

We consider the exchangeable fragmentation-coagulation (EFC) processes, where the coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and the fragmentations dislocate at finite rate an individual block into…

Whenever P is a proper definable forcing for adding a real, the countable support iteration of P has all the preservation properties it can possibly have, within a wide syntactically identified class of properties.

We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…

It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions…

Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the…

We set up a method for a recursive calculation of the effective potential which is applied to a cubic potential with imaginary coupling. The result is resummed using variational perturbation theory (VPT), yielding an exponentially fast…

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are…