Universality for random tensors

• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Titel: Universality for random tensors
• Verf.angabe: Razvan Gurau
• Ausgabe: Version v4
• E-Jahr: 2013
• Jahr: May 7, 2013
• Jahr des Originals: 2011
• Umfang: 51 S.
• Fussnoten: Version 1 vom 2. November 2011, Version 4 vom 6. Mai 2013 ; Gesehen am 29.09.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2013
• Band/Heft Quelle: (2013), Artikel-ID 1111.0519, Seite 1-51
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematical Physics
• Sach-SW: Mathematics - Probability
• K10plus-PPN: 180530156X

Abstract

We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N limit to the same limit as the distributional limit of a Gaussian tensor model. This generalizes the universality of random matrices to random tensors. We then prove a second, stronger, universality result. Under the weaker assumption that the joint probability distribution of tensor entries is invariant, assuming that the cumulants of this invariant distribution are uniformly bounded, we prove that in the large N limit the tensor again converges in distribution to the distributional limit of a Gaussian tensor model. We emphasize that the covariance of the large N Gaussian is not universal, but depends strongly on the details of the joint distribution.