A dynamical version of the SYK Model and the q-Brownian Motion

2019/05/30 by Miguel Pluma, Roland Speicher, Pluma, Miguel +1
Mathematics · #15B52 #46L54 #60E05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1905.12999

openalex publication_date 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate the limit of a dynamical version of the SYK model with the q-Brownian motion, a non-commutative deformation of classical Brownian motion. Furthermore, we extend the results for fluctuations to the multivariate setting and treat also higher correlation functions. The structure of our results for the sparse SYK random matrices resembles the formulas for higher order freeness for ordinary GUE random matrices.

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