Related papers: Cover time for countable Markov shifts
A novel technique of the measurement data processing is developed which allows to apply the rotating coil method for measurement of a dynamic magnetic field, periodic in time. The developed technique allows to obtain time-dependent…
Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…
This paper concentrates on the minimal hitting probability of continuous-time controlled Markov systems (CTCMSs) with countable state and finite admissible action spaces. The existence of an optimal policy is first proved. In particular,…
We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent…
We study the large time dynamics of a macroscopically large quantum systems under a sudden quench. We show that, first of all, for a generic system in the thermodynamic limit the Gibbs distribution correctly captures the large time dynamics…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…
When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy…
We study a random walk that prefers tou se unvisited edges in the context of random cubic graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being $\approx n\log n$ and $\approx \frac32n\log n$…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
For any stationary $\mZ^d$-Gibbs measure that satisfies strong spatial mixing, we obtain sequences of upper and lower approximations that converge to its entropy. In the case, $d=2$, these approximations are efficient in the sense that the…
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of available patterns such that the approximation of chaotic…
We propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…
For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the…