Related papers: Random models for singular SPDEs
In this paper we consider a super-renormalizable theory of massless QED in $(2+1)$ dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation we derive the Nielsen identities for the theory. Further, we…
This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole-Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid…
We study a general class of nonlinear Ginzburg-Landau SPDEs in infinite volume under weak nonlinearity scaling and with non-equilibrium initial data. We derive the KPZ equation as a continuum limit of these equations. This makes rigorous…
We prove a convergence result for a large class of random models that encompasses the case of the BPHZ models used in the study of singular stochastic PDEs. We introduce for that purpose a useful variation on the notion of regularity…
The focus of this work is the numerical approximation of time-dependent partial differential equations associated to initial-boundary value problems. This master dissertation is mostly concerned with the actual computation of the solution…
These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt. The main aim is to explain some aspects of the theory of "Regularity structures" developed…
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hilbert problem. Given a loop $\gamma(z), | z |=1$ of elements…
A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local…
We prove that a parabolically rescaled and suitably renormalised height function of a weakly asymmetric simple exclusion process on a circle converges to the Cole-Hopf solution of the KPZ equation. This is an analogue of the celebrated…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
We study the perturbative renormalization of quantum gauge theories in the Hopf algebra setup of Connes and Kreimer. It was shown by van Suijlekom (2007) that the quantum counterparts of gauge symmetries -- the so-called Ward--Takahashi and…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…
This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
It is well known that the mathematical structure underlying renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality of the field theory. Consequently, one…
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. Apart from deriving a basic existence and uniqueness…
We introduce a new concept of solution to the KPZ equation which is shown to extend the classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution map into a "universal" measurable map from the probability…
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…