2021/08/17 by Dimitrov, Evgeni, Knizel, Alisa
#33D45 #52C20 #82C41 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2108.07710
The goal of the paper is to introduce a new set of tools for the study of discrete and continuous β-corners processes. In the continuous setting, our work provides a multi-level extension of the loop equations (also called Schwinger-Dyson equations) for β-log gases obtained by Borot and Guionnet in (Commun. Math. Phys. 317, 447-483, 2013). In the discrete setting, our work provides a multi-level extension of the loop equations (also called Nekrasov equations) for discrete β-ensembles obtained by Borodin, Gorin and Guionnet in (Publications math' ematiques de l'IH' ES 125, 1-78, 2017).