Universality and borel summability of arbitrary quartic tensor models

• Verfasst von: Delepouve, Thibault [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Rivasseau, Vincent [VerfasserIn]
• Titel: Universality and borel summability of arbitrary quartic tensor models
• Verf.angabe: Thibault Delepouve, Razvan Gurau and Vincent Rivasseau
• E-Jahr: 2018
• Jahr: July 2, 2018
• Jahr des Originals: 2014
• Umfang: 30 S.
• Fussnoten: Version 1 vom 2. März 2014, Version 2 vom 29. November 2014 ; Version v2 ; Gesehen am 05.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2018
• Band/Heft Quelle: (2018), Artikel-ID 1403.0170, Seite 1-30
• DOI: doi:10.48550/arXiv.1403.0170
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 60B99
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematical Physics
• Sach-SW: Mathematics - Probability
• K10plus-PPN: 1805153269

Abstract

We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated Cauchy-Schwarz inequalities. Borel summability is proven, uniformly as the tensor size $N$ becomes large. Every cumulant is written as a sum of explicitly calculated terms plus a remainder, suppressed in $1/N$. Together with the existence of the large $N$ limit of the second cumulant, this proves that the corresponding sequence of probability measures is uniformly bounded and obeys the tensorial universality theorem.