In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. are given by a classical transition function that generates pair of conjugate linear operators Banach space bounded functions and finitely additive measures. We study sequences Cesaro means powers on the set probability It is proved all limit measures (points) such weak topology generat...

Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These feature special band eigenstates called many-body scar states in the energy spectrum. In this work we study fate two-dimensional lattice against random disorders. We show that both square and honeycomb can persist up to finite disorder strength, before eventually being erased by disorder....

We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates $I$, where $N^\varepsilon \le | I N^{1- \varepsilon}$, and prove it converges to Gaussian at every energy level, including edge, as $N\rightarrow \infty$. The key technical input is four-point decorrelation estimate eigenvectors with large component. Its proof an application maximum principle new ...

A fundamental question arising in queueing system analysis is whether a system is stable or unstable. For systems modelled by infinite Markov chain, we may study ergodicity and nonergodicity of the chains. Foster [6] showed that sufficient conditions for ergodicity are linked with the average drift, however. complications arise when multidimensional Markov chains are analysed. We shall present ...

3 2.3. The embedded discrete-time Hawkes process 5 2.4. Drift of a discrete-time Markov process 6 2.5. A digression on stochastic stability 7 3. Auxiliary Results 8 3.1. V−uniform ergodicity of the intensity of a Hawkes process 8 3.2. V−uniform ergodicity of the intensity of a multivariate Hawkes process 10 3.3. V-uniform ergodicity of a " birth-death " Hawkes process 13 4. Application to order...

This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has countably infinite state space. After establishing existence and uniqueness global weak solution via martingale approach under very mild conditions, paper next proves strong Feller property for regime-switching by killing technique together some resolvent transi...

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report, this parameter is calculated for fractional Brownian motion with a random change of time scale, often called "subordination." We show that this quantity is the same as the known continuous time random walks case.

We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and overview some the recent developments in mathematical Chaos.