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Free energy of spherical Coulomb gases with point charges
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We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the north and south poles, and with microscopic point charges inserted at the poles. These models can be interpreted as Coulomb gases on the complex plane with weakly confining potentials, where the associated droplet is the entire complex plane. For these models, we derive precise asymptotic expansions of the free energies, including the constant terms.
Forward citations
Cited by 2 Pith papers
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Asymptotics of the real eigenvalue distribution for the real spherical ensemble
For the real spherical ensemble, asymptotic formulas are derived for the probability of M real eigenvalues when M ~ N, M ~ sqrt(N), and M near the mean, with cross-regime matching and the leading p_{N,0} ~ e^{-sqrt(pi...
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Partition function of 2D Coulomb gases with radially symmetric potentials and a hard wall
For radially symmetric potentials at beta = 2, the log N coefficient in the hard-wall partition function is -1/4 for an annulus and -1/3 for a disk when the wall lies strictly inside the droplet, instead of the usual -1/12.
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