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  • 1 Département de Mathématiques, Université Paris XIII, 99 avenue J.B. Clément, F-93430 Villetaneuse, France
  • 2 Department of Mathematics, University of Utah, 155 South 1440 East, JWB 233, Salt Lake City, Utah 84112-0090, USA
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Abstract  

We study the large-time behavior of the charged-polymer Hamiltonian H n 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.

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