Related papers: Escape Rates Formulae and Metastability for Random…
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
We discuss how an eigenvalue perturbation formula for transfer operators of dynamical systems is related to exponential hitting time distributions and extreme value theory for processes generated by chaotic dynamical systems. We also list a…
Regular and rapid variation have been extensively studied in the literature and applied across various fields, particularly in extreme value theory. In this paper, we examine regular and rapid variation through the lens of generalized…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
Path integral techniques are used to understand the behaviour of a particle moving in a bistable potential well and acted upon by quasi-monochromatic external noise. In the limit of small diffusion coefficient, a steepest descent evaluation…
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\kappa$…
We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show…
We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are…
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…
We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckmann maps with singularities. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $\mu$…
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…
We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…
An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of moments, is present in the literature. Here we exploit equations determining wave speeds for that model. We find interesting results; for example,…