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 …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

We study the crossover from the macroscopic fluctuation theory (MFT), which describes one-
dimensional stochastic diffusive systems at late times, to the weak noise theory (WNT) …

We consider a class of nearest-neighbor weakly asymmetric mass conservative particle
systems evolving on Z, which includes zero-range and types of exclusion processes, starting …

We consider the motion of a particle under a continuum random environment whose
distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we …

We prove that the variance of the current across a characteristic is of order t 2/3 in a
stationary asymmetric simple exclusion process, and that the diffusivity has order t 1/3. The …

In many-particle diffusions, particles that move the furthest and fastest can play an outsized
role in physical phenomena. A theoretical understanding of the behavior of such extreme …

We consider n-point sticky Brownian motions: a family of n diffusions that evolve as
independent Brownian motions when they are apart, and interact locally so that the set of …

Random walk in a dynamic iid beta random environment, conditioned to escape at an
atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed …

We introduce a model of effective conformal quantum field theory in dimension $ d= 1+ 1$
coupled to stochastic noise, where Kardar-Parisi-Zhang (KPZ) class fluctuations can be …