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Sökning: LAR1:gu > Tidskriftsartikel > Chalmers tekniska högskola > Berman Robert 1976 > Övrigt vetenskapligt > (2011)

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1.
  • Berman, Robert, 1976-, et al. (författare)
  • Fekete points and convergence towards equilibrium measures on complex manifolds
  • 2011
  • Ingår i: Acta Mathematica. - 1871-2509. ; 207:1871-2509, s. 1-27
  • Tidskriftsartikel (övrigt vetenskapligt)abstract
    • Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth properties of balls of holomorphic sections, or equivalently as an asymptotic minimization of generalized Donaldson L-functionals. Our result yields in particular the proof of a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points, and it also gives the convergence of Bergman measures towards equilibrium for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed.
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2.
  • Berman, Robert, 1976- (författare)
  • Sharp asymptotics for Toeplitz determinants, fluctuations and the gaussian free field on a Riemann surface
  • 2011
  • Ingår i: preprint på arxiv.org.
  • Tidskriftsartikel (övrigt vetenskapligt)abstract
    • We consider canonical determinantal random point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric. In the higher genus (hyperbolic) cases these point processes may be defined in terms of automorphic forms. We establish strong exponential concentration of measure type properties involving Dirichlet norms of linear statistics. This gives an optimal Central Limit Theorem (CLT), saying that the fluctuations of the corresponding empirical measures converge, in the large N limt, towards the Laplacian of the Gaussian free field on X in the strongest possible sense. The CLT is also shown to be equivalent to a new sharp strong Szeg\"o type theorem for Toeplitz determinants in this context. One of the ingredients in the proofs are new Bergman kernel asymptotics providing exponentially small error terms in a constant curvature setting.
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Boucksom, Sebastien (1)
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Göteborgs universitet (2)
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