Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$
| Autor: | Nina C Snaith, Emilia Alvarez |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
15A52
11M06 Work (thermodynamics) Pure mathematics Mathematics - Number Theory Mathematics::Number Theory 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences Unitary state 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 010307 mathematical physics Logarithmic derivative 0101 mathematics Random matrix Mathematical Physics Mathematics Symplectic geometry |
| Popis: | We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, $N$, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices. 43 pages. This version has an added discussion and computation of lower order terms. It also contains implemented comments and suggestions from the referee for JMP. Accepted for publication in the Journal of Mathematical Physics |
| Databáze: | OpenAIRE |
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