Busemann functions and semi-infinite O'Connell-Yor polymers

Tom Alberts; Firas Rassoul-Agha; Mackenzie Simper

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arXiv · 1905.13353

Busemann functions and semi-infinite O'Connell-Yor polymers

Tom Alberts·Firas Rassoul-Agha·Mackenzie Simper

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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.

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Tom Alberts, Firas Rassoul-Agha, Mackenzie Simper. 2019-05-30. Busemann functions and semi-infinite O'Connell-Yor polymers. https://arxiv.org/abs/1905.13353

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