Yueyun Hu, Davar Khoshnevisan
Published 2009-11-19Version 1
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 $\{H_{[nt]}\}_{0\le t\le 1}$ behaves like a Brownian motion, time-changed by the intersection local-time process of an independent Brownian motion. Chung-type LILs are also discussed.
An alternative to the coupling of Berkes-Liu-Wu for strong approximations
Weak and strong approximations of reflected diffusions via penalization methods
The quenched limiting distributions of a charged-polymer model
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