129 citations · 316 across the 45 of their papers we have counts for
49 papers
Kruskal-style algorithm for Boltzmann equation molecule reduction
Yvain Bruned, Valentin Clarisse
We are interested in the molecule reduction algorithm used by Deng, Hani and Ma. This algorithm allows them to establish a rigidity theorem, which plays a central role in the long-…
Chain rule symmetry for singular SPDEs from multi-indices to decorated trees
Yvain Bruned
In these lecture notes, we review the recent results around the chain rule for the generalised KPZ equation and the geometric KPZ equation. We introduce the main ideas of Regularit…
On the equivalence between the Polchinski flow and the Connes-Kreimer approaches to perturbative renormalisation
Yvain Bruned, Paul Laubie, Aurélien Minguella
We prove a correspondence between the Polchinski flow and the Connes-Kreimer approaches to perturbative renormalisation, in the sense that the first yields the same renormalisation…
A general paracontrolled ansatz for singular SPDEs
Yvain Bruned, Nicolas Moench
We provide a general ansatz for the paracontrolled approach introduced by Gubinelli, Imkeller, Perkowski for treating singular SPDEs. The ansatz proposed covers a large class of eq…
Recentering with Malliavin derivative
Yvain Bruned, Aurélien Minguella
We provide an algebraic unification of the spectral gap proofs of the convergence of the renormalised model for regularity structures. We show that the key recentering map used in…
Kruskal-style algorithm for cubic Schrödinger equation molecule reduction
Yvain Bruned, Valentin Clarisse
We are interested in the molecule reduction algorithm introduced by Deng and Hani. They use this algorithm to establish a rigidity theorem, which plays a central role in the kineti…
Banach fixed point and flow approach for rough analysis
Yvain Bruned, Yingtong Hou, Paul Laubie +1
In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Baill…
Derivation of resonance-based schemes via normal forms
Yvain Bruned
In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butch…
Elementary differentials from multi-indices to rooted trees
Yvain Bruned, Paul Laubie
Rooted trees are essential for describing numerical schemes via the so-called B-series. They have also been used extensively in rough analysis for expanding solutions of singular S…
Birkhoff normal form via decorated trees
Jacob Armstrong-Goodall, Yvain Bruned
We derive an explicit tree based ansatz for the Birkhoff normal form up to any order in the context of Hamiltonian PDEs. To do so we make use of a tree based representation of iter…
Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures
Yvain Bruned, Yunhe Sheng, Rong Tang
In this paper, we study post-Lie deformations of a pre-Lie algebra, namely deforming a pre-Lie algebra into a post-Lie algebra. We construct the differential graded Lie algebra tha…
Resonances and computations
Yvain Bruned, Frédéric Rousset, Katharina Schratz
The computation of time dynamics arising in nonlinear time-dependent partial differential equations is an ongoing challenge in numerical analysis, especially once roughness comes i…
Renormalisation in the flow approach for singular SPDEs
Yvain Bruned, Aurélien Minguella
In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch. We introduce a general ansatz based on decorated trees for the solutio…
Flows driven by multi-indices Rough Paths
Carlo Bellingeri, Yvain Bruned, Yingtong Hou
In this work, we introduce a solution theory for scalar-valued rough differential equations driven by multi-indices rough paths. To achieve this task, we will show how the flow app…
Renormalising Feynman diagrams with multi-indices
Yvain Bruned, Yingtong Hou
In this work, we provide a method to obtain the renormalised measure in quantum field theory directly from the renormalisation of the expansion of the original measure. Our approac…
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…
Resonance based schemes for SPDEs
Jacob Armstrong-Goodall, Yvain Bruned
Resonance based numerical schemes are those in which cancellations in the oscillatory components of the equation are taken advantage of in order to reduce the regularity required o…