Related papers: Return times, recurrence densities and entropy for…
We consider a dynamical process in a network which distributes all particles (tokens) located at a node among its neighbors, in a round-robin manner. We show that in the recurrent state of this dynamics (i.e., disregarding a polynomially…
We show that if $G$ is a countable amenable group, then every stationary non-Gaussian symmetric $\alpha$-stable (S$\alpha$S) process indexed by $G$ is ergodic if and only if it is weakly-mixing, and it is ergodic if and only if its Rosinski…
In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary…
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…
We determine the $N\to \infty$ asymptotics of the expected value of entanglement entropy in $H_{1,N}\otimes H_{2,N}$, where $H_{1,N}$ and $H_{2,N}$ are the spaces of holomorphic sections of the $N$-th tensor powers of hermitian ample line…
We consider the return times dynamics to Bowen balls for continuous maps on metric spaces which have invariant probability measures with certain mixing properties. These mixing properties are satisfied for instance by systems that allow…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
We construct multiperiodic processes -- a simple example of stationary ergodic (but not mixing) processes over natural numbers that enjoy the vanishing entropy rate under a mild condition. Multiperiodic processes are supported on randomly…
A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any $\frac{1}{2}\leq \alpha\leq\beta\leq1$, there is a group $\Gamma$ with measure $\mu$ equidistributed on a finite…
The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…
In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
Generic quantum systems --as much as their classical counterparts-- pass arbitrarily close to their initial state after sufficiently long time. Here we provide an essentially exact computation of such recurrence times for generic…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
We are concerned with the first hitting times of the Bessel processes. We give explicit expressions for the densities by means of the zeros of the Bessel functions and show their asymptotic behavior.
Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$…
We study the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. We give a complete characterization of this relationship for i.i.d. processes over arbitrary…
We study the following interacting particle system. There are $\rho n$ particles, $\rho < 1$, moving clockwise ("right"), in discrete time, on $n$ sites arranged in a circle. Each site may contain at most one particle. At each time, a…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…