2019/12/15 by Aguirre, Ander, Soshnikov, Alexander, Sumpter, Joshua
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.1912.07110
We study limiting distribution of pair counting statistics of the form ∑1≤ i≠ j≤ N f(LN\*(θi-θj)) for the circular β-ensemble (CβE) of random matrices for sufficiently smooth test function f and LN=O(N). For β=2 and LN=N our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.