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- W93751490 abstract "We study determinantal point processes on a compact complex manifold X associated to an Hermitian metric on a a line bundle over X and a probability measure on X. When X is the complex projective line this setup contains the extensively studied (Hermitian, unitary and normal) random matrix ensembles. In general, the ensemble may be realized as the mathematical model of a quantum fermion gas on X in an exterior magnetic field. It is shown that in the many particle limit when L is replaced by a large tensor power (corresponding to the large rank limit in random matrix theory), the defining random measures describing the particle locations converge exponentially towards the corresponding equilibrium measure, defined in terms of the Monge-Ampere operator of complex pluripotential theory. More precisely, it is shown that the corresponding sequence of laws admits a large deviation principle with a good rate functional, whose unique minimum is the equilibrium measure. The entropy term in the rate functional turns out to be closely related to a well-known functional in Kahler-Einstein geometry." @default.
- W93751490 created "2016-06-24" @default.
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- W93751490 date "2008-12-23" @default.
- W93751490 modified "2023-09-27" @default.
- W93751490 title "Large deviations and entropy for determinantal point processes on complex manifolds" @default.
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