Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains when one of them satisfies a Wasserstein ergodicity condition. Our work is motivated by the recent ...

The strong coupling limit (βgauge = 0) of lattice QCD with staggered fermions enjoys the same non-perturbative properties as continuum QCD, namely confinement and chiral symmetry breaking. In contrast to the situation at weak coupling, the sign problem which appears at finite density can be brought under control for a determination of the full (μ ,T ) phase diagram by Monte Carlo simulations. F...

Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace H, we give a sufficient condition for the convergence to 0 on H of a general product. Our result is applied to obtain a condition for the weak ergodicity of...

For any stochastic matrix A of order n, denote its eigenvalues as λ1(A), . . . , λn(A), ordered so that 1 = |λ1(A)| ≥ |λ2(A)| ≥ . . . ≥ |λn(A)|. Let cT be a row vector of order n whose entries are nonnegative numbers that sum to n. Define S(c), to be the set of n × n row-stochastic matrices with column sum vector cT . In this paper the quantity λ(c) = max{|λ2(A)||A ∈ S(c)} is considered. The ve...

SUMMARY The Monte Carlo Expectation Maximization (MCEM) algorithm (Wei and Tanner (1991)), a stochas-tic version of EM, is a versatile tool for inference in incomplete data models, especially when used in combination with MCMC simulation methods. Examples of applications include, among many others: regression with missing values (Wei and Tanner (1991)), time-series analysis (Chan and Ledolter (...

Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The interreaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary interreaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic re...

We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependen...

We investigate the influence of spin-orbit interaction on ballistic transport through chaotic cavities by using semiclassical methods. Our approach is based on the Landauer formalism IBM J. Res. Dev. 1, 223 1957 ; 32, 306 1988 and the Fisher-Lee relations Phys. Rev. B 23, 6851 1981 , appropriately generalized to spin-orbit interaction, and a semiclassical representation of Green’s functions. We...