Strong approximations in a charged-polymer model

Yueyun Hu and Davar Khoshnevisan

Abstract. We study the large-time behavior of the charged-polymer Hamiltonian Hn of Kantor and Kardar [Bernoulli case] and Derrida, Griffiths, and Higgs [Gaussian case], using strong approximations to Brownian motion. Our results imply, among other things, that in one dimension the process {H[nt]}0≤t≤1 behaves like a Brownian motion, time-changed by the intersection local-time process of an independent Brownian motion. Chung-type LILs are also discussed.

Keywords. Charged polymers, strong approximations, local time.

AMS Classification (2000) Primary: 60K35; Secondary: 60K37.

Support. Research supported in part by the National Science Foundation grant DMS-0706728.

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Yueyun Hu
Départment de Mathématiques
Université Paris 13
99 avenue J-B Clé'ment, F-93430, Villetaneuse, France
Davar Khoshnevisan
Department of Mathematics
University of Utah
155 S, 1400 E JWB 233
Salt Lake City, UT 84112-0090, U.S.A.

Last Update: November 19, 2009
© 2009 - Yueyun Hu and Davar Khoshnevisan