Sharp asymptotics for Fredholm Pfaffians related to interacting particle systems and random matrices
| Autor: | Roger Tribe, Oleg Zaboronski, Will FitzGerald |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
annihilating Brownian motions FOS: Physical sciences Pfaffian Lambda Ginibre ensemble Szego’s theorem Combinatorics symbols.namesake Matrix (mathematics) FOS: Mathematics QA 60B20 60K35 82C22 Eigenvalues and eigenvectors Mathematical Physics Mathematics Particle system 60B20 Probability (math.PR) Pfaffian point processes Mathematical Physics (math-ph) Riemann hypothesis Distribution (mathematics) symbols Statistics Probability and Uncertainty 82C22 Random matrix Mathematics - Probability |
| Zdroj: | Electron. J. Probab. |
| ISSN: | 1083-6489 |
| Popis: | It has been known since the pioneering paper of Mark Kac, that the asymptotics of Fredholm determinants can be studied using probabilistic methods. We demonstrate the efficacy of Kac' approach by studying the Fredholm Pfaffian describing the statistics of both non-Hermitian random matrices and annihilating Brownian motions. Namely, we establish the following two results. Firstly, let $\sqrt{N}+\lambda_{max}$ be the largest real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). Consider the limiting $N\rightarrow \infty$ distribution $\mathbb{P}[\lambda_{max} Comment: 14 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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