Related papers: Perturbations of Markov Chains
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine…
We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the…
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\k{e}g\l owski (2015). Here, we turn our attention to the study of Markov consistency and…
These lectures describe the use of effective field theories to extrapolate results from the parameter region where numerical simulations of lattice QCD are possible to the physical parameters (physical quark masses, infinite volume,…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that the potential and…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…
Perturbative approaches have often been used to include the effects of ground-state correlations in extended theories of the random-phase approximation. Validity of such approaches is investigated for a solvable model where comparison with…
Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…
I present an outline of chiral perturbation theory and discuss some recent developments in the field.
We theoretically investigate the correlation functions of the phase of a light wave propagating through a turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a second-order nonlinear term. Based…
Markov chain analysis is a key technique in formal verification. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not --…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
A pattern of partial resummation of perturbation theory series inspired by analytical continuation is discussed for some physical observables.
This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation…
Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…