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The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove…

Probability · Mathematics 2019-09-25 Tobias Johnson , Matthew Junge

We maximize the production of biogas in a gradostat at steady state. The physical decision variables are the water, substrate, and biomass entering each tank and the flows through the interconnecting pipes. Our main technical focus is the…

Optimization and Control · Mathematics 2021-02-04 Josh Taylor , Alain Rapaport

We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the…

Statistical Mechanics · Physics 2014-09-18 Chikashi Arita

It is known that the Dobrushin's ergodicity coefficient is one of the effective tools to study a behavior of non-homogeneous Markov chains. In the present paper, we define such an ergodicity coefficient of a positive mapping defined on…

Functional Analysis · Mathematics 2013-11-05 Farrukh Mukhamedov

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…

Optimization and Control · Mathematics 2012-05-18 Serdar Yüksel , Sean P. Meyn

In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional…

Operator Algebras · Mathematics 2019-11-26 Xinxin Chen , Adam Dor-On , Langwen Hui , Christopher Linden , Yifan Zhang

We derive the second order rates of joint source-channel coding, whose source obeys an irreducible and ergodic Markov process when the channel is a discrete memoryless, while a previous study solved it only in a special case. We also…

Information Theory · Computer Science 2024-09-10 Ryo Yaguchi , Masahito Hayashi

We study a fairly general class of time-homogeneous stochastic evolutions driven by noises that are not white in time. As a consequence, the resulting processes do not have the Markov property. In this setting, we obtain constructive…

Probability · Mathematics 2009-02-12 M. Hairer

The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding…

Information Theory · Computer Science 2022-05-23 Nir Weinberger

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…

Dynamical Systems · Mathematics 2014-11-18 Ivan Werner

Understanding causal relationships between variables is a fundamental problem with broad impact in numerous scientific fields. While extensive research has been dedicated to learning causal graphs from data, its complementary concept of…

Machine Learning · Computer Science 2024-03-12 Jiaqi Zhang , Kirankumar Shiragur , Caroline Uhler

This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres…

Probability · Mathematics 2007-05-23 Persi Diaconis , Laurent Saloff-Coste

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…

Quantum Physics · Physics 2024-02-13 Tibor Rakovszky , Sarang Gopalakrishnan , Curt von Keyserlingk

Non-Markovian stochastic processes are ubiquitous in biology. Nevertheless, we lack a general framework for quantifying historical dependencies. In this Letter, we propose an information-theoretic approach to decompose history dependence in…

Statistical Mechanics · Physics 2025-12-23 Matthew P. Leighton , Christopher W. Lynn

Constraint-based methods are one of the main approaches for causal structure learning that are particularly valued as they are asymptotically guaranteed to find a structure that is Markov equivalent to the causal graph of the system. On the…

Machine Learning · Computer Science 2021-05-24 Ehsan Mokhtarian , Sina Akbari , AmirEmad Ghassami , Negar Kiyavash

Stochastic Resonance in single voltage-dependent ion channels is investigated within a three state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an…

Biological Physics · Physics 2007-05-23 I. Goychuk , P. Hanggi , J. L. Vega , S. Miret-Artes

A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…

Statistical Mechanics · Physics 2021-03-18 Tristan Gautié , Naftali R. Smith

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…

Statistics Theory · Mathematics 2020-04-28 Simon Byrne , A. Philip Dawid

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…

Probability · Mathematics 2019-06-24 François Bienvenu , Florence Débarre , Amaury Lambert

We study Markovian random products on a large class of "m-dimensional" connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and…

Dynamical Systems · Mathematics 2018-04-18 Lorenzo J. Díaz , Edgar Matias