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Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

Published online by Cambridge University Press:  15 May 2003

Pierre Del Moral  and
L. Miclo
Pierre Del Moral
Affiliation:
LSP, UMR 5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France; e-mail:
L. Miclo
Affiliation:
LSP, UMR 5583 du CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France; e-mail:
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Abstract

We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue ofSchrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V. These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine a class of modelsextending the hard obstacle modelof K. Burdzy, R. Holyst and P. March and including the Moran type scheme presented by the authors in a previous work. We provide precise uniform estimates with respect to the time parameter and we analyze the fluctuations of continuous time particle models.

Keywords

Feynman–Kac formulaSchrödinger operatorspectral radiusLyapunov exponentspectral decompositionsemigroups on a Banach spaceinteracting particle systemsgeneticalgorithmsasymptotic stabilitycentral limit theorems.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 171 - 208
Copyright
© EDP Sciences, SMAI, 2003

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References

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