We study ordinary differential equations (ODEs) with vector fields given by general Schwartz
distributions, and we show that if we perturb such an equation by adding an “infinitely …

We consider the stochastic differential equation on ℝ d given by d X t= b (t, X t) dt+ d B t,
where B is a Brownian motion and b is considered to be a distribution of regularity>− 1 2. We …

We consider a semilinear parabolic partial differential equation in R _+ * 0, 1^ d R+× 0, 1 d,
where d= 1, 2 d= 1, 2 or 3, with a highly oscillating random potential and either …

Paracontrolled calculus and regularity structures I Page 1 c⃝2021 The Mathematical Society of
Japan J. Math. Soc. Japan Vol. 73, No. 2 (2021) pp. 553–595 doi: 10.2969/jmsj/81878187 …

The reconstruction theorem tackles the problem of building a global distribution, on ℝ d or
on a manifold, for a given family of sufficiently coherent local approximations. This theorem …

A tourist’s guide to regularity structures Page 1 A tourist’s guide to regularity structures I.
BAILLEUL & M. HOSHINO Abstract. We give a short essentially self-contained treatment of the …

A tourist’s guide to regularity structures and singular stochastic PDEs Page 1 EMS Surv. Math.
Sci. (Online first) DOI 10.4171/EMSS/87 © 2025 European Mathematical Society Published …

We construct random Schr\" odinger operators, called Anderson Hamiltonians, with Dirichlet
and Neumann boundary conditions for a fairly general class of singular random potentials …

We prove a general equivalence statement between the notions of models and modeled
distributions over a regularity structure, and paracontrolled systems indexed by the regularity …

We study a regularization by noise phenomenon for the continuous parabolic Anderson
model with a potential shifted along paths of fractional Brownian motion. We demonstrate …