Related papers: Escape rates for Gibbs measures
We study the limiting behavior of $r$-maximum distance minimizers and the asymptotics of their $1$-dimensional Hausdorff measures as $r$ tends to zero in several contexts, including situations involving objects of fractal nature.
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…
This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $\nu$ associated with such a random walk. We first establish a link of the form $\dim \nu \leq…
We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position $x_0$. In particular, we present a remarkably compact derivation of the time-dependent…
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…
We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
We derive the asymptotic behavior of hitting probability at small target of size $O(\epsilon)$ for reflected Brownian motion in domains with suitable smooth boundary conditions, where the boundary of domain contains both reflecting part,…
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…
We consider the action of Mandelbrot multiplicative cascades on probability measures supported on a symbolic space. For general probability measures, we obtain almost a sharp criterion of non-degeneracy of the limiting measure; it relies on…
In this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape of mass, the measure theoretic entropy, and the entropy at infinity of the…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related…
The Josephson junction noise detector measures the skewness of non-Gaussian noise via the asymmetry of the rate of escape from the zero-voltage state upon reversal of the bias current. The feedback of this detector on the noise generating…
We prove the existence of an ergodic measure with full Hausdorff dimension for a class of nonlinear nonconformal skew-product transformations. In order to do so we establish a variational principle for the topological pressure of certain…
We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies…
Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the…
We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an…
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased…