Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Large deviations for random hives and the spectrum of the sum of two random matrices
Speaker: Hariharan Narayanan, TIFR
Date: November 1, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let $X_n$, $Y_n$ be independent random Hermitian matrices from unitarily invariant distributions with spectra $\lambda_n$, $\mu_n$ respectively. We define $||\cdot||_\mathcal I$ to be a certain specific norm. We prove that the following limit exists, when $\lambda_n$ and $\mu_n$ have suitably defined limits when $n$ tends to infinity. $$ \lim_{n \to \infty} \frac{\ln P[||\operatorname{Spec}(X_n+Y_n)-\nu_n||_\mathcal I < \epsilon]}{n^2}. $$ We interpret this limit in terms of the surface tension of continuum limits of the discrete hives defined by Knutson and Tao. This is joint work with Scott Sheffield.
Title of Talk: Large deviations for random hives and the spectrum of the sum of two random matrices
Speaker: Hariharan Narayanan, TIFR
Date: November 1, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let $X_n$, $Y_n$ be independent random Hermitian matrices from unitarily invariant distributions with spectra $\lambda_n$, $\mu_n$ respectively. We define $||\cdot||_\mathcal I$ to be a certain specific norm. We prove that the following limit exists, when $\lambda_n$ and $\mu_n$ have suitably defined limits when $n$ tends to infinity. $$ \lim_{n \to \infty} \frac{\ln P[||\operatorname{Spec}(X_n+Y_n)-\nu_n||_\mathcal I < \epsilon]}{n^2}. $$ We interpret this limit in terms of the surface tension of continuum limits of the discrete hives defined by Knutson and Tao. This is joint work with Scott Sheffield.