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 …

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 …

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 consider the solution of the stochastic heat equation\cal Z= 1 2\partial_X^ 2\cal Z-\cal Z ̇
W with delta function initial condition\cal Z (T= 0, X)= X= 0 whose logarithm, with appropriate …

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

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 …

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 …

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

We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one
dimension, with an initial condition which physically corresponds to the motion of a …