The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour
(July 7–24, 2002), by the Professors Pitman, Tsirelson and Werner …

The conjectured limit of last passage percolation is a scale-invariant, independent,
stationary increment process with respect to metric composition. We prove this for Brownian …

We provide a framework for proving convergence to the directed landscape, the central
object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that …

We discuss Brownian analogues of a celebrated theorem, due to Burke, which states that
the output of a (stable, stationary) M/M/1 queue is Poisson, and the related notion of …

We characterize the law of the partition function of a Brownian directed polymer model in
terms of a diffusion process associated with the quantum Toda lattice. The proof is via a …

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

We survey a number of models from physics, statistical mechanics, probability theory and
combinatorics, which are each described in terms of an orthogonal polynomial ensemble …

We study some path transformations related to Pitman's theorem [28, Th. 1.3] on Brownian
motion and the three-dimensional Bessel process. We relate these to the Littelmann path …

The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …