Related papers: Perfect simulation for a class of positive recurre…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
We present a recurrence-transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities associated to the increments of the chain, defined via the…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
The first aim of this paper is to introduce a class of Markov chains on $\mathbb{Z}_+$ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation…
We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…
We examine the problem of exactly or approximately counting all perfect matchings in hereditary classes of nonbipartite graphs. In particular, we consider the switch Markov chain of Diaconis, Graham and Holmes. We determine the largest…
We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is either positive recurrent of null recurrent, and we give an…
Certain non-uniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations, we extend the simplest such chain to next-to-nearest neighbour (NNN) couplings. It…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…
Given access to a single long trajectory generated by an unknown irreducible Markov chain $M$, we simulate an $\alpha$-lazy version of $M$ which is ergodic. This enables us to generalize recent results on estimation and identity testing…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past. A version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…
We consider general Markov chains with discrete time in an arbitrary measurable (phase) space and homogeneous in time. Markov chains are defined by the classical transition function which within the framework of the operator treatment…
Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…