7 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…
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…
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…
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…
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…
On the Radical of Multiperfect Numbers and Applications
Nithin Kavi, Xinyi Zhang, Viraj Jayam +1
It is conjectured that for a perfect number We prove bounds on the radical of multiperfect number depending on its abundancy index. Assum…