We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the is (i) expanding and (ii) well-spread, (iii) certain random variable on boundary of ball has tail. As applications, we show that volume intersection Hamming, Johnson spaces symmetric groups decay exponentially as their centers drift apart. To verify conditio...

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the ...

The rapid decay of the viral load after drug treatment in patients infected with human immunodeficiency virus type 1 (HIV-1) has been shown to result from the rapid loss of infected cells due to their high turnover, with a generation time of around 1 to 2 days. Traditionally, viral decay dynamics after drug treatment is investigated using models of differential equations in which both the death...

We present a set of new, semi-analytical solutions to simulate three-dimensional contaminant transport subject to first-order chain-decay reactions. The aquifer is assumed to be areally semi-infinite, but finite in thickness. The analytical solution can treat the transformation of contaminants into daughter products, leading to decay chains consisting of multiple contaminant species and various...

We prove a lower bound on the rate of relaxation to equilibrium in the H1 norm for a thin film equation. We find a two stage relaxation, with power law decay in an initial interval, followed by exponential decay, at an essentially optimal rate, for large times. The waiting time until the exponential decay sets in is explicitly estimated.

This paper addresses the question of change of decay rate from exponential to algebraic for diffusive evolution equations. We show how the behaviour of the spectrum of the Dirichlet Laplacian in the two cases yields the passage from exponential decay in bounded domains to algebraic decay or no decay at all in the case of unbounded domains. It is well known that such rates of decay exist: the pu...

We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationaryGaussian processes. This result allows us to find explicitly the rates of exponential decay of the error probabilities of type I and type II for Neyman–Pearson tests. Furthermore, we obtain the analogue of classical results on asymptotic efficiency of tests such as Stein’s lemma an...

We show that at a second order phase transition, of 4 φ like system, a necessary condition for stretched exponential decay of the time dependent structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of the structure factor is obtained and shown to yield stretched exponential decay under very reasonable conditions.