129 citations · 316 across the 45 of their papers we have counts for
8 papers · 1 filter
Cancellations for dispersive PDEs with random initial data
Yvain Bruned, Leonardo Tolomeo
In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The ma…
Derivation of normal forms for dispersive PDEs via arborification
Yvain Bruned
In this work, we propose a systematic derivation of normal forms for dispersive equations using decorated trees introduced in arXiv:2005.01649. The key tool is the arborification m…
Low regularity symplectic schemes for stochastic NLS
Jacob Armstrong-Goodall, Yvain Bruned
We introduce a class of symplectic resonance based schemes for Schrödinger's equation in dimension one, building on the work in [1] wherein resonance based numerical schemes were d…
Symmetries for the gKPZ equation via multi-indices
Carlo Bellingeri, Yvain Bruned
In this work, we study the two main symmetries for the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the Itô Isometry. We consider the equation in the full-su…
Multi-indices coproducts from ODEs to singular SPDEs
Yvain Bruned, Yingtong Hou
In this work, we introduce explicit formulae for the coproducts at play for multi-indices in ODEs and in singular SPDEs. The two coproducts described correspond to versions of the…
Chain rule symmetry for singular SPDEs
Yvain Bruned, Vladimir Dotsenko
We characterise the chain rule symmetry for the geometric stochastic heat equations in the full subcritical regime for Gaussian and non-Gaussian noises. We show that the renormalis…
Multi-indice B-series
Yvain Bruned, Kurusch Ebrahimi-Fard, Yingtong Hou
We propose a novel way to study numerical methods for ordinary differential equations in one dimension via the notion of multi-indice. The main idea is to replace rooted trees in B…
Quasi-generalised KPZ equation
Yvain Bruned, Máté Gerencsér, Usama Nadeem
We derive the renormalised equation for the quasi-generalised KPZ equation with space-time white noise. We complement the program initiated by Gerencsér and Hairer for solving quas…