2024/02/26 by Sayan Das, Das, Sayan, Christian Serio +1
Environmental Science · #60K35 #82B41 #82D60 #Chemical Synthesis and Characterization #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2402.16834
openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit description, which can be interpreted as two random walks conditioned softly never to intersect. This limiting law is a stationary measure for the polymer on the anti-diagonal path. The starting point of our analysis is an embedding of the free energy into the half-space log-gamma line ensemble recently constructed by Barraquand, Corwin, and Das. Given the Gibbsian line ensemble structure, the main contribution of our work lies in developing a route to access and prove convergence to stationary measures via line ensemble techniques. Our argument relies on a description of the limiting behavior of two softly non-intersecting random walk bridges around their starting point, a result established in this paper that may be of independent interest.