These are lecture notes for a mini-course given at the St. Petersburg School in Probability
and Statistical Physics in June 2012. Topics include integrable models of random growth …

We introduce a new disorder regime for directed polymers in dimension 1+1 that sits
between the weak and strong disorder regimes. We call it the intermediate disorder regime …

We consider two models for directed polymers in space‐time independent random media
(the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random …

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 propose a new definition of the Gaussian multiplicative chaos and an approach based
on the relation of subcritical Gaussian multiplicative chaos to randomized shifts of a …

We consider directed polymers in random environment in the critical dimension d= 2,
focusing on the intermediate disorder regime when the model undergoes a phase transition …

We compute the one-point probability distribution for the stationary KPZ equation (ie initial
data H (0, X)= B (X) H(0,X)=B(X), for B (X) a two-sided standard Brownian motion) and show …

This paper studies the stochastic heat equation with multiplicative noises of the form uW,
where W is a mean zero Gaussian noise and the differential element uW is interpreted both …

This article attempts to give a short survey of recent progress on a class of elementary
stochastic partial differential equations (for example, stochastic heat equations) driven by …

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions
ensuring that a sequence of multi-linear polynomials of independent random variables …