Applied Math Seminar
Winter Quarter 2002
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday
January 11, 2001


Jared Bronski
University of Illinois
Urbana-Champaign

Passive Scalar intermittency, Eigenvalue Asymptotics,
and Small Ball Estimates.

Abstract:

In this talk we present some work on the transport of a passive scalar by a random velocity field. In a particular model (originally introduced by Majda, and generalized by Vanden Eijnden) we are able to compute the rate of decay of the tails of the limiting probability distribution function for the advected scalar in terms of the large n (semiclassical) behavior of the eigenvalues of a certain integral operator. We are able to use some approximate bases to derive tight asymptotics for these eigenvalues. The same calculation also gives the (previously unknown) tight constant for the small (L_2) ball estimates for a fractional Brownian motion.

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