Single eigenvalue fluctuations of general Wigner-type matrices

Autor: Benjamin Landon, Patrick Lopatto, Philippe Sosoe
Rok vydání: 2023
Předmět:
Zdroj: Probability Theory and Related Fields.
ISSN: 1432-2064
0178-8051
DOI: 10.1007/s00440-022-01181-6
Popis: We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem for linear spectral statistics on larger scales via resolvent techniques and show that for certain classes of test functions, the leading-order contribution to the variance agrees with the GOE/GUE cases.
Comment: v4: incorporated referee comments, v3: paper re-organized, v2: corrected misprints, improved presentation
Databáze: OpenAIRE
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