A strong limit theorem in the Kac-Zwanzig model

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Abstract

A strong limit theorem is proved for a version of the well-known Kac-Zwanzig model, in which a 'distinguished' particle is coupled to a bath of N free particles through linear springs with random stiffness. It is shown that the evolution of the distinguished particle, albeit generated from a deterministic set of dynamical equations, converges pathwise towards the solution of an integro-differential equation with a random noise term. Both the canonical and microcanonical ensembles are considered.

Original languageEnglish (US)
Pages (from-to)145-162
Number of pages18
JournalNonlinearity
Volume22
Issue number1
DOIs
StatePublished - Jan 1 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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