Tail bounds for the O'Connell-Yor polymer (Q6595716)

This paper gives a detailed analysis of the tail behavior of the O'Connell-Yor (OY) polymer, a key model in the Kardar-Parisi-Zhang (KPZ) universality class. The authors establish precise upper and lower bounds for the left and right tails of the polymer's partition function in the moderate deviations regime. Employing probabilistic and geometric methods, they achieve results that surpass those obtained through traditional integrable techniques, highlighting the robustness of their approach. This work complements prior research by providing the first detailed analysis of the left-tail behavior of the OY polymer, which had remained unexplored even with integrable methods.\N\NThis paper adapts techniques like geodesic watermelons to the polymer setting and compensating for linear corrections in the free energy. The results are rigorously derived and systematically presented, making them both robust and broadly applicable to other KPZ-class models. While primarily theoretical, the paper's implications could extend to other domains, bridging gaps between integrable and non-integrable approaches. A discussion on potential applications or numerical illustrations could enhance its reach to a wider audience. Overall, this is a significant contribution to the study of directed polymers in random environments and the broader KPZ universality framework.