385 citations · 4.3k across the 93 of their papers we have counts for
38 papers · 1 filter
Loop Vertex Representation for Cumulants, Part I: Bounds on Free Energy with Sources
Vincent Rivasseau
In this paper we construct cumulants for stable random matrix models with single trace interactions of arbitrarily high even order. We obtain explicit and convergent expansions for…
Honeycomb Hubbard Model at van Hove Filling
Vincent Rivasseau, Zhituo Wang
This paper is devoted to the rigorous study of the low temperature properties of the two-dimensional weakly interacting Hubbard model on the honeycomb lattice in which the renormal…
Honeycomb Hubbard Model at van Hove Filling II: Lower Bounds of the Self-Energy
Vincent Rivasseau, Zhituo Wang
In this paper we complete the proof that the honeycomb Hubbard model with renormalized chemical potential is {\it not} a Fermi liquid in the mathematically precise sense of S…
Can we make sense out of "Tensor Field Theory"?
Vincent Rivasseau, Fabien Vignes-Tourneret
We continue the constructive program about tensor field theory through the next natural model, namely the rank five tensor theory with quartic melonic interactions and propagator i…
Constructive Matrix Theory for Higher Order Interaction II: Hermitian and Real Symmetric Cases
Thomas Krajewski, Vincent Rivasseau, Vasily Sazonov
This paper provides the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmet…
Melonic Turbulence
Stéphane Dartois, Oleg Evnin, Luca Lionni +2
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weak…
Constructive Matrix Theory for Higher Order Interaction
Thomas Krajewski, Vincent Rivasseau, Vasily Sazonov
This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation fo…
Constructive tensor field theory: The model
Vincent Rivasseau, Fabien Vignes-Tourneret
We continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator invers…
Loop Vertex Expansion for Higher Order Interactions
Vincent Rivasseau
This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail…
Constructive Tensor Field Theory
Vincent Rivasseau
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathem…
Random Tensors and Quantum Gravity
Vincent Rivasseau
We provide an informal introduction to tensor field theories and to their associated renormalization group. We focus more on the general motivations coming from quantum gravity tha…
Note on the Intermediate Field Representation of Phi^2k Theory in Zero Dimension
Luca Lionni, Vincent Rivasseau
This expanded version corrects some misprints of the first version, details completely the poof of Borel-Leroy summability and for in the complex case provides a new improved…
Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
Remi Cocou Avohou, Vincent Rivasseau, Adrian Tanasa
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation…
Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
Valentin Bonzom, Thibault Delepouve, Vincent Rivasseau
Ordinary tensor models of rank are dominated at large by tree-like graphs, known as melonic triangulations. We here show that non-melonic contributions can be enhance…
Constructive Tensor Field Theory: The Model
Thibault Delepouve, Vincent Rivasseau
We build constructively the simplest tensor field theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse o…
Corrected Loop Vertex Expansion for Phi42 Theory
Vincent Rivasseau, Zhituo Wang
This paper is an extended erratum to J. Math. Phys.53, 042302 (2012) and arXiv:1104.3443, in which the classic construction and Borel summability of the phi^4_2 Euclidean quantum f…
The Multiscale Loop Vertex Expansion
Razvan Gurau, Vincent Rivasseau
The loop vertex expansion (LVE) is a constructive technique which uses only canonical combinatorial tools and no space-time dependent lattices. It works for quantum field theories…
Generalized constructive tree weights
Vincent Rivasseau, Adrian Tanasa
The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on s…
How to Resum Feynman Graphs
Vincent Rivasseau, Zhituo Wang
In this paper we reformulate in a simpler way the combinatoric core of constructive quantum field theory We define universal rational combinatoric weights for pairs made of a graph…
Spheres are rare
Vincent Rivasseau
We prove that triangulations of homology spheres in any dimension grow much slower than general triangulations. Our bound states in particular that the number of triangulations of…
Parametric Cutoffs for Interacting Fermi Liquids
Margherita Disertori, Jacques Magnen, Vincent Rivasseau
We introduce a new multiscale decomposition of the Fermi propagator based on its parametric representation. We prove that the corresponding sliced propagator obeys the same direct…
Constructive Renormalization for Theory with Loop Vertex Expansion
Vincent Rivasseau, Zhituo Wang
In this paper we construct the 2 dimensional Euclidean quantum field theory using the method of loop vertex expansion. We reproduce the results of standard constructive theor…
Introduction to the Renormalization Group with Applications to Non-Relativistic Quantum Electron Gases
Vincent Rivasseau
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are differ…
How are Feynman graphs resumed by the Loop Vertex Expansion?
Vincent Rivasseau, Zhituo Wang
The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the theory in n…