It is well-known that Control Theory was founded by N. Wiener in 1948 ([349]). After that, this
theory was greatly extended to various complicated setting and widely used in sciences and …

This book provides an introduction to the theory of stochastic partial differential equations
(SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability …

Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

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 prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models
with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A …

We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …

We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of
paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer …

We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …

Motivated by the paradigm of reservoir computing, we consider randomly initialized
controlled ResNets defined as Euler-discretizations of neural controlled differential …

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