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 ...