Mélange : exemples, applications
Merging for time inhomogeneous finite Markov chains. I: Singular values and stability.
Metastability of the three dimensional Ising model on a torus at very low temperatures.
Mixing time for the Ising model : a uniform lower bound for all graphs
Consider Glauber dynamics for the Ising model on a graph of n vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least nlog n/f(Δ), where Δ is the maximum degree and f(Δ) = Θ(Δlog2Δ). Their result applies to more general spin systems, and in that generality, they showed that some dependence on Δ is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any n-vertex graph is at least (1/4 + o(1))nlog n....
Mixing time of the Rudvalis shuffle.
Mixing times for Markov chains on wreath products and related homogeneous spaces.
Mixing times for random walks on finite lamplighter groups.
Moderate deviations for stable Markov chains and regression models.
Monotone measures of ergodicity for Markov chains.
Monotonicity and comparison results for nonnegative dynamic systems. Part I: Discrete-time case
In two subsequent parts, Part I and II, monotonicity and comparison results will be studied, as generalization of the pure stochastic case, for arbitrary dynamic systems governed by nonnegative matrices. Part I covers the discrete-time and Part II the continuous-time case. The research has initially been motivated by a reliability application contained in Part II. In the present Part I it is shown that monotonicity and comparison results, as known for Markov chains, do carry over rather smoothly...
Monte Carlo simulation of Markov chain steady-state distribution.
Most random walks on nilpotent groups are mixing
Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.
Necessary and sufficient optimality conditions for average reward of controlled Markov chains
Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles.
Non-Homogeneous Markov Chains: Tail Idempotents, Tail Sigma-Fields and Basis.
Non-homogeneous Markov chains with a finite state space and a Doeblin type theorem.
Nonlinear Markov processes in big networks
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...
Note: random-to-front shuffles on trees.
Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime
This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...
Occupation laws for some time-nonhomogeneous Markov chains.