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Abstract
We consider a Gaussian rotationally invariant ensemble of random real totally symmetric tensors with independent normally distributed entries, and estimate the largest eigenvalue of a typical tensor in this ensemble by examining the rate of growth of a random initial vector under successive applications of a nonlinear map defined by the random tensor. In the limit of a large number of dimensions, we observe that a simple form of melonic dominance holds, and the quantity we study is effectively determined by a single Feynman diagram arising from the Gaussian average over the tensor components. This computation suggests that the largest tensor eigenvalue in our ensemble in the limit of a large number of dimensions is proportional to the square root of the number of dimensions, as it is for random real symmetric matrices.
Original language  English 

Article number  66 
Number of pages  18 
Journal  Letters in Mathematical Physics 
Volume  111 
Issue number  3 
DOIs  
Publication status  Published  Jun 2021 
Bibliographical note
v2: comments and references added, accepted for publicationKeywords
 mathph
 hepth
 math.MP
 math.PR
 math.SP
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Dive into the research topics of 'Melonic dominance and the largest eigenvalue of a large random tensor'. Together they form a unique fingerprint.Projects
 1 Active

SRP8: Strategic Research Programme: HighEnergy Physics at the VUB
D'Hondt, J., Van Eijndhoven, N., Craps, B. & Buitink, S.
1/11/12 → 31/10/24
Project: Fundamental