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Pair Dependent Linear Statistics for Circular Beta Ensemble
Probability| Speaker: | Alexander Soshnikov, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~soshniko/ |
| Location: | Zoom lecture |
| Start time: | Thu, Oct 29 2020, 4:10PM |
We study limiting distribution of pair counting statistics of the form $\sum_{1\leq i\neq j\leq N} f(L_N\*(θ_i-θ_j))$ for the circular $\beta$-ensemble (CβE) of random matrices for sufficiently smooth test function $f$ and $L_N=O(N).$ For $\beta=2$ and $L_N=N$ our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.
Based on joint work with my graduate students Ander Aguirre and Josh Sumpter
(arXiv:1912.07110 math.PR and arXiv:2004.01345 math.PR).
Note different day: Thursday instead of Wednesday