Related papers: Hitting times and periodicity in random dynamics
In this paper we study the quenched distributions of hitting times for a class of random dynamical systems. We prove that hitting times to dynamically defined cylinders converge to a Poisson point process under the law of random equivariant…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
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…
Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this definition we derive an explicit formula for…
The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the…
We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a…
We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive…
We prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures $\{\mu_\omega\}_{\omega\in\Omega}$, where the `driving space' $\Omega$ is equipped with a probability measure which is…
Hitting rate and escape rate are two examples of recurrence laws for a dynamical system, and a general limit connects them. We show that for both Gibbs-Markov systems or any systems with the $\phi$-mixing measure, for a sequence of nested…
There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one…
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general…
Recent progress in the understanding of quenched invariance principles (QIP) for a continuous-time random walk on $\mathbb{Z}^d$ in an environment of dynamical random conductances is reviewed and extended to the $1$-dimensional case. The…
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential…
Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all…
We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of…