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 …

These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

We develop in this work a general version of paracontrolled calculus that allows to treat
analytically within this paradigm a whole class of singular partial differential equations with …

We provide in this work a semigroup approach to the study of singular PDEs, in the line of
the paracontrolled approach developed recently by Gubinelli, Imkeller and Perkowski …

We study the lattice approximations to the dynamical Φ 3 4 model by paracontrolled
distributions proposed in [Forum Math. Pi 3 (2015) e6]. We prove that the solutions to the …

In this work, we show a convergence result for the discrete formulation of the generalised
KPZ equation∂ tu=(Δ u)+ g (u)(∇ u) 2+ k (∇ u)+ h (u)+ f (u) ξ t (x), where ξ is real-valued, Δ …

We prove an invariance principle for the two-dimensional lattice parabolic Anderson model
with small potential. As applications we deduce a Donsker type convergence result for a …

We develop a Fourier analytic approach to rough path integration, based on the series
decomposition of continuous functions in terms of Schauder functions. Our approach is …

We sharpen in this work the tools of paracontrolled calculus in order to provide a complete
analysis of the parabolic Anderson model equation and Burgers system with multiplicative …

We construct the Dirichlet form associated with the dynamical Φ4 3 model obtained in [23, 7]
and [37]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear …