We consider a discrete polynuclear growth (PNG) process and prove a functional limit
theorem for its convergence to the Airy process. This generalizes previous results by …

This is an introductory survey of the Kardar-Parisi-Zhang equation (KPZ). The first chapter
provides a non-rigorous background to the equation and to some of the many models which …

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the
general parameter dependent distribution between two sets of eigenvalues with two different …

We review the Airy processes—their formulation and how they are conjectured to govern the
large time, large distance spatial fluctuations of 1-D random growth models. We also …

We consider the multi-point equal time height fluctuations of the one-dimensional
polynuclear growth model in half-space. For special values of the nucleation rate at the …

In a celebrated paper, Dyson shows that the spectrum of an n× n random Hermitian matrix,
diffusing according to an Ornstein–Uhlenbeck process, evolves as n noncolliding Brownian …

We develop a theory of multilevel distributions of eigenvalues which complements Dyson's
threefold ˇ D 1; 2; 4 approach corresponding to real/complex/quaternion matrices by ˇ D 1 …

In (J. Stat. Phys. 132, 275-290, 2008) Borodin and P\'ech\'e introduced a generalization of
the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of …

We introduce a generalization of the extended Airy kernel with two sets of real parameters.
We show that this kernel arises in the edge scaling limit of correlation kernels of …

We show that classical integrable models of last passage percolation and the related
nonintersecting random walks converge uniformly on compact sets to the Airy line …