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math.PR2025
Critical fluctuations of last passage percolation with thick boundaries
Elnur Emrah, Patrik L. Ferrari, Min Liu
We consider the exponential last passage percolation (LPP) with thick two-sided boundary that consists of a few inhomogeneous columns and rows. Ben Arous and Corwin previously stud…
math.PR2024
Quasi-geodesics in integrable and non-integrable exclusion processes
Patrik L. Ferrari, Min Liu
Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of th…
math.PR2024
Exact decay of the persistence probability in the Airy process
Patrik L. Ferrari, Min Liu
We consider the Airy process, which is the limit process in KPZ growth models with flat and non-random initial conditions. We study the persistence probability, namely the prob…