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The Kac master equation with unbounded collision rate

Journal article
Authors Bernt Wennberg Mattias Sundén Markov Processes and Related Fields 15 2 125-148 1024-2953 2009 Department of Mathematical Sciences, Mathematical Statistics Department of Mathematical Sciences, Mathematics 125-148 en Brownian motion, collision kernel, Feller processes, innitesimal generator, Kac model, Laplace - Beltrami operator, Markov process, semigroup, spectral gap Mathematical Analysis, Mathematical statistics, Other Mathematics

Abstract

The Kac model is a Markov jump process on the sphere $\sum_{j=1}^{N} v_j^2$. The model was conceived as model for an N-particle system with pairwise interactions, and hence the jumps involve only pairs of coordinates, $(v_i, v_j )$. This paper deals with Kac models with unbounded jump rates. We prove that the processes are Feller processes, and introduce a diusion approximation that is useful for numerical simulation of the processes. We also study the spectral gap of the Markov generators, using the methods developed by Carlen, Carvalho and Loss.

Page Manager: Webmaster|Last update: 9/11/2012
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