Geodesic
The extremal landscape for the C$\beta $E ensemble
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e1

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C$\beta $E ensemble. We prove convergence in distribution of the centered maxima (of the real and imaginary parts) toward the sum of a Gumbel variable and another independent variable, which we characterize as the total mass of a ‘derivative martingale’. We also provide a description of the landscape near extrema points. 
Paquette, Elliot; Zeitouni, Ofer. The extremal landscape for the C$\beta $E ensemble. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e1. doi: 10.1017/fms.2024.129
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