6 papers
Hitting time mixing for random -cycles
Chen Shang, Jiahe Shen, Jiyue Zeng +1
In this paper, we study the random walk on the symmetric group generated by the conjugacy class of -cycles, where . We prove that the wa…
The discrete periodic Pitman transform: invariances, braid relations, and Burke properties
Eva R. Engel, Benjamin Jasper Kra-Caskey, Oleksandr Lazorenko +5
We develop the theory of the discrete periodic Pitman transform, first introduced by Corwin, Gu, and the fifth author. We prove that the discrete periodic Pitman transform satisfie…
Stationary Log-Gamma Polymer in Half-Space
Jiyue Zeng, Xinyi Zhang
We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal acros…
Convergence of Half-Space Last Passage Percolation Away from the Boundary to the Directed Landscape
Xinyi Zhang
In this note, we prove convergence of the half-space exponential last passage percolation (LPP) model, away from the boundary, to the directed landscape. Our approach couples the h…
Convergence from the Log-Gamma Polymer to the Directed Landscape
Xinyi Zhang
We define the log-gamma sheet and the log-gamma landscape in terms of the 2-parameter and 4-parameter free energy of the log-gamma polymer model and prove that they converge to the…
Near-the-Axis Universality in Last Passage Percolation
Sam McKeown, Xinyi Zhang
This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal flu…