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math.PR2023★ 1 cited
Free energy and fluctuations in the random normal matrix model with spectral gaps
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study large expansions for the partition function of a Coulomb gas $$Z_n=\frac 1 {π^n}\int_{\mathbb{C}^n}\prod_{1\le i<j\le n}|z_i-z_j|^2\prod_{i=1}^n e^{-nQ(z_i)}\, d^2 z_i…
math-ph2023
Random normal matrices: eigenvalue correlations near a hard wall
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant and that the number …
math-ph2023
Eigenvalues of truncated unitary matrices: disk counting statistics
Yacin Ameur, Christophe Charlier, Philippe Moreillon
Let be an truncation of an Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of . We prove that as…