These notes are based on lectures delivered by the authors at a Langeoog seminar of
SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience of …

Abstract We study a (1+ 1)-dimensional directed polymer in a random environment on the
integer lattice with log-gamma distributed weights. Among directed polymers, this model is …

We establish a fundamental connection between the geometric Robinson–Schensted–
Knuth (RSK) correspondence and GL (N, R)-Whittaker functions, analogous to the well …

The divide and conquer method is a common strategy for handling massive data. In this
article, we study the divide and conquer method for cubic-rate estimators under the massive …

We study the last-passage growth model on the planar integer lattice with exponential
weights. With boundary conditions that represent the equilibrium exclusion process as seen …

This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite
geodesics in directed planar last-passage percolation with exponential weights. The …

We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …

We prove that the variance of the current across a characteristic is of order t 2/3 in a
stationary asymmetric simple exclusion process, and that the diffusivity has order t 1/3. The …

These lecture notes discuss several related features of the exactly solvable two-dimensional
corner growth model with exponentially distributed weights. A key property of this model is …

We establish estimates for the coalescence time of semi-infinite directed geodesics in the
planar corner growth model with iid exponential weights. There are four estimates: upper …