We prove that the free energy of the log-gamma polymer between lattice points (1, 1) and
(M, N) converges to the GUE Tracy–Widom distribution in the M 1/3 scaling, provided that …

In this paper, we study large time large deviations for the height function $\mathfrak {h}(x, t) $
of the $ q $-deformed polynuclear growth introduced in ABW22 [arXiv: 2108.06018]. We …

We consider the asymmetric simple exclusion process (ASEP) on Z started from step initial
data and obtain the exact Lyapunov exponents for H 0 (t), the integrated current of ASEP. As …

Consider the asymmetric nearest-neighbor exclusion process (ASEP) on ${\mathbb Z} $ with
single particle drift $\gamma> 0$, starting from a Bernoulli product invariant measure …

This thesis investigates the geometry of polymers and other miscellaneous results in the
Kardar-Parisi-Zhang (KPZ) universality class. Directed polymers have enjoyed a rich history …

Path properties of KPZ models Sayan Das Submitted in partial fulfillment of the
requirements for the degree of Doctor of Philoso Page 1 Path properties of KPZ models …