论文信息 - Central Limit Theorem for $C\beta E$ Pair Dependent Statistics in Mesoscopic Regime

Central Limit Theorem for $C\beta E$ Pair Dependent Statistics in Mesoscopic Regime

We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i\neq j}f(L_N(\theta_i-\theta_j))$ for arbitrary $\beta>0$ in the mesoscopic regime $L_N=O(N^{2/3-\epsilon})$.

Ander Aguirre | Alexander Soshnikov

[1] Gershon Wolansky,et al. Optimal Transport , 2021 .

[2] C. Villani. Optimal Transport: Old and New , 2008 .

[3] A. Soshnikov,et al. Pair dependent linear statistics for CβE , 2020, Random Matrices: Theory and Applications.

[4] Mesoscopic central limit theorem for the circular $\beta $-ensembles and applications , 2019, 1902.06611.

[5] R. Killip,et al. Matrix models for circular ensembles , 2004, math/0410034.

[6] Stein's method and the multivariate CLT for traces of powers on the classical compact groups , 2010, 1012.3730.

[7] Christian Linear statistics of the circular β-ensemble , stein ’ s method , and circular Dyson Brownian motion , 2016 .

[8] F. Dyson. Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[9] Kurt Johansson,et al. Multivariate normal approximation for traces of random unitary matrices , 2020, The Annals of Probability.

[10] P. Diaconis,et al. On the eigenvalues of random matrices , 1994, Journal of Applied Probability.

[11] P. Gallagher. Pair correlation of zeros of the zeta function. , 1985 .

[12] M. R. Leadbetter,et al. Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[13] Xavier Gourdon,et al. Distribution of the zeros of the Riemann Zeta function , 2004 .

[14] F. Dyson. Correlations between eigenvalues of a random matrix , 1970 .