Busemann functions and semi-infinite O'Connell-Yor polymers
Probability
2019-12-03 v2
Abstract
We prove that given any fixed asymptotic velocity, the finite length O'Connell-Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a Markovian property of the quenched polymer this reduces to showing the existence of Busemann functions: almost sure limits of ratios of random point-to-point partition functions. The key ingredients are the Burke property of the O'Connell-Yor polymer and a comparison lemma for the ratios of partition functions. We also show the existence of infinite length limits in the Brownian last passage percolation model.
Cite
@article{arxiv.1905.13353,
title = {Busemann functions and semi-infinite O'Connell-Yor polymers},
author = {Tom Alberts and Firas Rassoul-Agha and Mackenzie Simper},
journal= {arXiv preprint arXiv:1905.13353},
year = {2019}
}
Comments
22 pages, 1 figure, version accepted for publication at Bernoulli