TY - JOUR

T1 - Asymptotics of Karhunen-Loeve eigenvalues and tight constants for probability distributions of passive scalar transport

AU - Bronski, Jared C.

PY - 2003/7

Y1 - 2003/7

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-003-0835-3

DO - 10.1007/s00220-003-0835-3

M3 - Article

AN - SCOPUS:0043245223

SN - 0010-3616

VL - 238

SP - 563

EP - 582

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -