Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the
minimum of a set of random variables. This is an important problem for any time-series and …

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 …

The stochastic partial differential equation proposed nearly three decades ago by Kardar,
Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here …

We study the directed polymer of length t in a random potential with fixed endpoints in
dimension 1+ 1 in the continuum and on the square lattice, by analytical and numerical …

We study the fluctuations of the largest eigenvalue λ max of N× N random matrices in the
limit of large N. The main focus is on Gaussian β ensembles, including in particular the …

We provide the first exact calculation of the height distribution at arbitrary time t of the
continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial …

The distribution function of the free-energy fluctuations in one-dimensional directed
polymers with δ-correlated random potential is studied by mapping the replicated problem to …

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 …

We study a dark energy scenario in the presence of a tachyon field ϕ with potential V (ϕ)
and a barotropic perfect fluid. The cosmological dynamics crucially depends on the …

We calculate analytically the probability of large deviations from its mean of the largest
(smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary …