Related papers: Escape rates for Gibbs measures
We exhibit a singularly perturbed parabolic problems for which the asymptotic behavior can be described by an one-dimensional ordinary differential equation. We estimate the continuity of attractors in the Hausdorff metric by rate of…
We prove that the Hausdorff dimension of an average conformal repeller is stable under random perturbations. Our perturbation model uses the notion of a bundle random dynamical system.
In this short note, we propose a new and short approach to polynomial escape rates, which can be applied to various open systems with intermittency. The tool of our approach is the maximal large deviations developed in \cite{mldp}.
Borrowing and extending the method of images we introduce a theoretical framework that greatly simplifies analytical and numerical investigations of the escape rate in open dynamical systems. As an example, we explicitly derive the exact…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
We apply the escape-rate formalism to compute the shear viscosity in terms of the chaotic properties of the underlying microscopic dynamics. A first passage problem is set up for the escape of the Helfand moment associated with viscosity…
We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in H\"older singularity sets of a Borel measure. This…
We study the relation between metric entropy and escape of mass for the Hilbert modular spaces with the action of a diagonal element.
We prove that a partially hyperbolic attracting set for a C2 vector field, having slow recurrence to equilibria, supports an ergodic physical/SRB measure if, and only if, the trapping region admits non-uniform sectional expansion on a…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on…
In this paper, we show that Gibbs measures on self-conformal sets generated by a $C^{1+\alpha}$ conformal IFS on $\mathbb{R}^d$ satisfying the OSC are exponentially mixing. We exploit this to obtain essentially sharp asymptotic counting…
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…
In this note we prove that every weak Gibbs measure for an asymptotically additive sequences is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure…
This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…
The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when standard signal processing tools can be prohibitive. We show that the prescriptions for the…
In this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase). We use thermodynamic multifractal formalism to calculate the…