Abstract:
We prove Gaussian fluctuations for pair-counting statistics of the form Σ1⩽i≠j⩽Nf(θi−θj) for the circular unitary ensemble of random matrices in the large-N limit under the condition that the variance increases slowly as N increases.
Keywords:
random matrix, circular unitary ensemble, pair-counting statistics,
central limit theorem.
Citation:
A. Aguirre, A. B. Soshnikov, “A note on pair-dependent linear statistics with a slowly increasing variance”, TMF, 205:3 (2020), 502–512; Theoret. and Math. Phys., 205:3 (2020), 1682–1691