Universality and borel summability of arbitrary quartic tensor models
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
July 2, 2018
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| In: |
Arxiv
Year: 2014, Pages: 1-30 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1403.0170
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| Author Notes: | Thibault Delepouve, Razvan Gurau and Vincent Rivasseau |
MARC
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| 520 | |a 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. | ||
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