Abstract
We derive upper and lower bounds for the right and left tails of the O’Connell-Yor polymer of the correct order of magnitude via probabilistic and geometric techniques in the moderate deviations regime. This result has not previously been obtained even by the methods of integrable probability. The inputs of our work are an identity for the generating function of a two-parameter model of Rains and Emrah-Janjigian-Seppäläinen, and the geometric techniques of Ganguly-Hegde and Basu-Ganguly-Hammond-Hegde. As an intermediate result we obtain strong tail estimates for the transversal fluctuation of the polymer path from the diagonal.
Acknowledgments
B.L. thanks Amol Aggarwal and Duncan Dauvergne for helpful and illuminating discussions. The work of B.L. is supported by an NSERC Discovery grant and a Connaught New Researcher Award. The work of P.S. is partially supported by NSF grants DMS-1811093 and DMS-2154090. We thank the referees for their careful reading and numerous suggestions which have greatly improved the paper.
Citation
Benjamin Landon. Philippe Sosoe. "Tail bounds for the O’Connell-Yor polymer." Electron. J. Probab. 29 1 - 47, 2024. https://doi.org/10.1214/24-EJP1162
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