Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using explicit formalism of Lanczos algorithm, usually known as forward scattering approximation in this context, we compute Krylov state (spread) complexity typical generated by time evolution PXP Hamiltonian, hosting such states. We show for N\'eel revives an approximate sense, wh...

We establish characterization results for the ergodicity of symmetric α–stable (SαS) and α–Fréchet max–stable stationary random fields. We first show that the result of Samorodnitsky [35] remains valid in the multiparameter setting, i.e., a stationary SαS (0 < α < 2) random field is ergodic (or equivalently, weakly mixing) if and only if it is generated by a null group action. The similarity of...

We will discuss the recurrence on the state space of the adaptive MCMC algorithm using some examples. We present the ergodicity properties of adaptive MCMC algorithms under the minimal recurrent assumptions, and show the Weak Law of Large Numbers under the same conditions. We will analyze the relationship between the recurrence on the product space of state space and parameter space and the erg...

We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, ergodicity with isometric coefficients. show that there exist transformations are coefficients but not weakly doubly ergodic; hence these notions equivalent for measure. also give type III? examples such systems, 0<??1. prove under certain hypotheses, systems mixing along the way we a...

We state and prove new properties about Doeblin’s ergodicity coefficient for finite Markov chains. We show that this coefficient satisfies a sub-multiplicative type inequality (analogous to the Markov-Dobrushin’s ergodicity coefficient), and provide a novel but elementary proof of Doeblin’s characterization of weak-ergodicity for non-homogeneous chains. Using Doeblin’s coefficient, we illustrat...

A criterion of joint ergodicity of several sequences of transformations of a probability measure space X of the form T φi(n) i is given for the case where Ti are commuting measure preserving transformations of X and φi are integer valued generalized linear functions, that is, the functions formed from conventional linear functions by an iterated use of addition, multiplication by constants, and...

We consider the time-inhomogeneous Prendiville model with failures and repairs. The property of weak ergodicity is considered, estimates rate convergence for main probabilistic characteristics are obtained. Several examples considered showing how such obtained limiting themselves constructed.

We consider the second-order asymptotic properties of‎  ‎the bootstrap of L_1 regression estimators by looking at‎ ‎the difference between the L_1 estimator and ‎its first-order approximation‎, ‎where the latter‎ ‎is the minimizer of a quadratic approximation to the‎ ‎L_1 objective function‎. ‎It is shown that the bootstrap ‎distribution of the normed difference does not converge‎ ‎(eit...