We consider denumerable state nonhomogeneous Markov decision processes and extend results from both denumerable state homogeneous and finite state nonhomogeneous problems. We show that, under weak ergodicity, accumulation points of finite horizon optima (termed algorithmic optima) are average cost optimal. We also establish the existence of solution horizons. Finally, an algorithm is presented ...

Quantum many-body scars (QMBSs) are a paradigm of weak ergodicity breaking with direct technological applications. The authors show that QMBSs ubiquitous in quantum link formulations gauge theories, opening the door to large venue models where can be explored. They demonstrate not an artifact these formulations, rather, they may inherent feature ideal theory itself.

This survey is based on a series of talks I gave at the conference " Dynamical systems and Diophantine approximation " at l'Instut Henri Poincaré in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundanc...

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include correspondence weak solutions equations, well-posedness, regularity estimates, exponential ergodicity, long time large d...

Abstract The nonlinear filter associated with the discrete time signal-observation model (Xk,Yk) is known to forget its initial condition as k →∞ regardless of the observation structure when the signal possesses sufficiently strong ergodic properties. Conversely, it stands to reason that if the observations are sufficiently informative, then the nonlinear filter should forget its initial condit...

Weak mixing is an important property for group extensions because its absence is the principal obstruction to lifting a large number of stronger mixing properties. Whether or not an extension is weakly mixing can be determined by studying the sub-extension corresponding to the quotient by the commutator subgroup. Several conditions equivalent to weak mixing are given. In particular, an extensio...

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed and has a parameter with which the estimator is optimized to reduce its bias. It is shown that est...

We consider an L-Wasserstein type distance ρ on the configuration space ΓX over a Riemannian manifold X, and we prove that ρ-Lipschitz functions are contained in a Dirichlet space associated with a measure on ΓX satisfying certain natural assumptions. These assumptions are in particular fulfilled by the classical Poisson measures and by a large class of tempered grandcanonical Gibbs measures wi...

This paper is another case study in the program of logically analyzing proofs to extract new (typically effective) information (‘proof mining’). We extract explicit uniform rates of metastability (in the sense of T. Tao) from two ineffective proofs of a classical theorem of F.E. Browder on the convergence of approximants to fixed points of nonexpansive mappings as well as from a proof of a theo...