Strong approximations in a charged-polymer model
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.
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