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In this paper, we consider weak horseshoe with bounded-gap-hitting times. For a flow $(M,phi)$, it is shown that if the time one map $(M,phi_1)$ has weak horseshoe with bounded-gap-hitting times, so is $(M,phi_tau)$ for all $tau eq 0$. In addition, we prove that for an affine homeomorphsim of a compact metric abelian group, positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.
We generalize the notion of strong stationary time and we give a representation formula for the hitting time to a target set in the general case of non-reversible Markov processes.
In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of strong metastability time is introduced to describe the lo
For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powe
In this paper, we consider the renormalization operator $mathcal R$ for multimodal maps. We prove the renormalization operator $mathcal R$ is a self-homeomorphism on any totally $mathcal R$-invariant set. As a corollary, we prove the existence of the