Strong approximations in a charged-polymer model
Yueyun Hu, Davar Khoshnevisan
TL;DR
This paper investigates the large-time behavior of a charged-polymer Hamiltonian using strong approximations to Brownian motion, revealing its convergence to a time-changed Brownian motion and discussing Chung-type laws of the iterated logarithm.
Contribution
It provides new strong approximation results for the charged-polymer Hamiltonian, connecting it to Brownian motion and intersection local times, which was not previously established.
Findings
The process behaves like a Brownian motion time-changed by intersection local time.
Results imply convergence in distribution to a Brownian motion in one dimension.
Chung-type laws of the iterated logarithm are established.
Abstract
We study the large-time behavior of the charged-polymer Hamiltonian 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 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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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering