Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations

Hultgren, Jakob

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 11-65.

On introduit un cadre thermodynamique pour des équations Monge–Ampères sur des tores réelles, qui est inspiré par des constructions en géometrie complexe. On démontre la convergence en loi pour les processus aléatoires correspondants, expliquant les liens avec des équations de Monge–Ampères complexes sur des variétés abéliennes et le transport optimal.

Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge–Ampère equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge–Ampère equations on abelian varieties and optimal transport.

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