We introduce a new notion of “regularity structure” that provides an algebraic framework
allowing to describe functions and/or distributions via a kind of “jet” or local Taylor expansion …

We introduce an approach to study certain singular partial differential equations (PDEs)
which is based on techniques from paradifferential calculus and on ideas from the theory of …

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 …

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

Offers an introduction to large deviations. This book is divided into two parts: theory and
applications. It presents basic large deviation theorems for iid sequences, Markov …

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

Kinetic limits for waves in a random medium Page 1 Kinetic limits for waves in a random
medium Guillaume Bal∗ Tomasz Komorowski † Lenya Ryzhik ‡ September 30, 2010 Contents …

Disorder is one of the predominant topics in science today. The present text is devoted to the
mathematical studyofsome particular cases ofdisordered systems. It deals with waves in …

In this paper linear stochastic evolution equations driven by infinite-dimensional fractional
Brownian motion are studied. A necessary and sufficient condition for the existence and …

From May 8 to May 19th of 2006, the Department of Mathematics at the University of Utah
hosted a minicourse on some modern topics in stochastic partial differential equations …