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math.CV2022
Chebyshev potentials, Fubini--Study metrics, and geometry of the space of Kähler metrics
Chenzi Jin, Yanir A. Rubinstein
The Chebyshev potential of a Kähler potential on a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the…
math.FA2022
The Nazarov proof of the non-symmetric Bourgain--Milman inequality
Vlassis Mastrantonis, Yanir A. Rubinstein
In 2012, Nazarov used Bergman kernels and Hormander's estimates for the -equation to give a new proof of the Bourgain--Milman theorem for symmetric convex bodie…
math.PR2022
On large deviation principles and the Monge--Ampère equation (following Berman, Hultgren)
Yanir A. Rubinstein
This is mostly an exposition, aimed to be accessible to geometers, analysts, and probabilists, of a fundamental recent theorem of R. Berman with recent developments by J. Hultgren,…