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 …

Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in develo** a theory for its properties (such as distribution …

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of
a wealth of classical stochastic models. Surprisingly, KPZ universality was recently …

Understanding universal aspects of quantum dynamics is an unresolved problem in
statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg …

Random quantum circuits yield minimally structured models for chaotic quantum dynamics,
which are able to capture, for example, universal properties of entanglement growth. We …

In this article we review classical and recent results in anomalous diffusion and provide
mechanisms useful for the study of the fundamentals of certain processes, mainly in …

With focus on anharmonic chains, we develop a nonlinear version of fluctuating
hydrodynamics, in which the Euler currents are kept to second order in the deviations from …

These lecture notes give a short review of methods such as the matrix ansatz, the additivity
principle or the macroscopic fluctuation theory, developed recently in the theory of non …

This paper contains an exposition of both recent and rather old results on determinantal
random point fields. We begin with some general theorems including proofs of necessary …

We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other things) …