Related papers: Bounding the coarse graining error in hidden Marko…
The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general…
Markov state models (MSMs)---or discrete-time master equation models---are a powerful way of modeling the structure and function of molecular systems like proteins. Unfortunately, MSMs with sufficiently many states to make a quantitative…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…
It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function space whose members…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to…
The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…
Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility-measured by the statistical…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium…