2019/10/08 by Valentin Bahier, Bahier, Valentin, Joseph Najnudel +1
Computer Science · Mathematics · #15B52 #60F05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1910.03621
openalex publication_date 2019/10/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We study the limiting behavior of smooth linear statistics of the spectrum of\nrandom permutation matrices in the mesoscopic regime, when the permutation\nfollows one of the Ewens measures on the symmetric group. If we apply a smooth\nenough test function f to all the determinations of the eigenangles of the\npermutations, we get a convergence in distribution when the order of the\npermutation tends to infinity. Two distinct kinds of limit appear: if f(0)\≠\n0, we have a central limit theorem with a logarithmic variance, and if f(0) =\n0, the convergence holds without normalization and the limit involves a\nscale-invariant Poisson point process.\n