Quasi-states and quasi-measures

Metastable states, quasi-stationary distributions and soft measures

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypotheses for Markov chains on a finite configuration space in some asymptotic regime. By comparing restricted ensemble and quasi-stationary measures, and introducing soft measures as interpolation between the two, we prove asymptotic exponential exit law and, on a generally different time scale, asympto...

Conditioned, quasi-stationary, restricted measures and escape from metastable states

We study the asymptotic hitting time τ (n) of a family of Markov processes X to a target set G when the process starts from a trap defined by very general properties. We give an explicit description of the law of X conditioned to stay within the trap, and from this we deduce the exponential distribution of τ . Our approach is very broad —it does not require reversibility, the target G does not ...

Quasi-copulas and signed measures

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0, 1]n . We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n ≥ 3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0, 1]n . © 2010 Elsevier B.V. All rights reserved.

Free Quasi-free States

To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the construction of quasi-free states on the CAR and CCR algebras. We show that under certain conditions, our C∗-algebras are simple, and the free quasi-free states are unique. The corresponding von Neuma...

Admissible vector fields and quasi-invariant measures∗