In this topical review we consider stochastic processes under resetting, which have attracted
a lot of attention in recent years. We begin with the simple example of a diffusive particle …

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 …

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

Characterizing how entanglement grows with time in a many-body system, for example, after
a quantum quench, is a key problem in nonequilibrium quantum physics. We study this …

We map the dynamics of entanglement in random unitary circuits, with finite onsite Hilbert
space dimension q, to an effective classical statistical mechanics, and develop general …

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

We introduce a new concept of solution to the KPZ equation which is shown to extend the
classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution …

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar
widely accepted framework for non-equilibrium statistical mechanics (NESM) remains …

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 …

Macdonald processes are probability measures on sequences of partitions defined in terms
of nonnegative specializations of the Macdonald symmetric functions and two Macdonald …