Archive ouverte HAL – Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble

Bertrand Lacroix-A-Chez-Toine ¹ Jeyson Andres Monroy GarzonChristopher Sebastian Hidalgo CalvaAnupam Kundu ² Satya N. Majumdar ¹ Jeyson Andrés Monroy GarzónIsaac Pérez Castillo ³ Satya Majumdar ¹ Gregory Schehr ¹

Bertrand Lacroix-A-Chez-Toine, Jeyson Andres Monroy Garzon, Christopher Sebastian Hidalgo Calva, Anupam Kundu, Satya N. Majumdar, et al.. Intermediate deviation regime for the full eigenvalue statistics in the complex Ginibre ensemble. Physical Review E , American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.012137⟩. ⟨hal-02291786⟩

We study the Ginibre ensemble of $N \times N$ complex random matrices and compute exactly, for any finite $N$, the full distribution as well as all the cumulants of the number $N_r$ of eigenvalues within a disk of radius $r$ centered at the origin. In the limit of large $N$, when the average density of eigenvalues becomes uniform over the unit disk, we show that for $0

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
• 3. Departamento de Sistemas Complejos, Instituto de Física, UNAM