On the operator norm of a random matrix with a polynomially decaying metric correlation structure
MATHPHYS ANALYSIS SEMINAR
Date
Thursday, January 21, 2021 16:15 - 17:15
Speaker
Jana Reker (IST Austria)
Location
online via Zoom
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Laszlo Erdös
Contact
In this talk, we consider a $N\timesN$ Hermitian random matrix with a polynomially decaying metric correlation structure.
Trivial a priori bound shows that the operator norm of this model is stochastically dominated by $\sqrt{N}$. However, by calculating the trace of the moments of the matrix and using the summable decay of the cumulants, the estimate on the norm can be improved to a bound of order one. This is a rotation project with László Erdös.