Related papers: Hitting times and periodicity in random dynamics

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…

It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…

We discuss limit distributions for hitting-time functions of certain exceptional families of asymptotically rare events for ergodic probability preserving transformations. The abstract core is an inducing argument. The latter applies, for…

Consider a class of null-recurrent randomly biased walks on a super-critical Gaton-Watson tree. We obtain the rates of convergence of the local times and the quenched local probability for the biased walk in the sub-diffusive case. These…

In this paper, we study the behaviour of the longest common substring for random subshifts of finite type (for dynamicists) or of the longest common substring for random sequences in random environments (for probabilists). We prove that,…

Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on…

Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…

We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…

We take a one-dimensional tight binding chain with periodic boundary condition and put a particle in an arbitrary Bloch state, then quench it by suddenly changing the potential of an arbitrary site. In the ensuing time evolution, the…

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in…

Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…

We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

We consider a biased random walk in positive random conductances on $\mathbb{Z}^d$ for $d\geq 5$. In the sub-ballistic regime, we prove the quenched convergence of the properly rescaled random walk towards a Fractional Kinetics.

In this paper we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an iid fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary…

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…

We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…

For flows whose return map on a cross section has sufficient mixing property, we show that the hitting time distribution of the flow to balls is exponential in limit. We also establish a link between the extreme value distribution of the…

The principal aim of the present work is to explore limit theorems for small random perturbations of dynamical systems with periodic impulse effects, in the limit of vanishing noise intensity. We start with a system whose time evolution is…