Related papers: Discrete Capacity and Higher-order Differences of …
By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are…
We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
We study Markov bases of decomposable graphical models consisting of primitive moves (i.e., square-free moves of degree two) by determining the structure of fibers of sample size two. We show that the number of elements of fibers of sample…
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
The main goal of this paper is to develop an estimate for the entropy of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We present here the detailed analytical study of the entropy for the…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a…
In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among…
Disordered pinning models deal with the (de)localization tran- sition of a polymer in interaction with a heterogeneous interface. In this paper, we focus on two models where the inhomogeneities at the interface are not independent but given…
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…
We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and…
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…
We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small spheres distributed in an $\veps$-periodic network. The asymptotic…