Asymptotics of Karhunen-Loeve eigenvalues and tight constants for probability distributions of passive scalar transport

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Abstract

In this paper we study the asymptotics of the probability distribution function for a certain model of freely decaying passive scalar transport. In particular we prove rigorous large n, or semiclassical, asymptotics for the eigenvalues of the covariance of a fractional Brownian motion. Using these asymptotics, along with some standard large deviations results, we are able to derive tight asymptotics for the rate of decay of the tails of the probability density for a generalization of the Majda model of scalar intermittency originally due to Vanden Eijnden. We are also able to derive asymptotically tight estimates for the closely related problem of small L2 ball probabilities for a fractional Brownian motion.

Original languageEnglish (US)
Pages (from-to)563-582
Number of pages20
JournalCommunications in Mathematical Physics
Volume238
Issue number3
DOIs
StatePublished - Jul 1 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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