Biorthogonal ensembles with two-particle interactions

@article{Claeys2014BiorthogonalEW,
  title={Biorthogonal ensembles with two-particle interactions},
  author={Tom Claeys and Stefano Romano},
  journal={Nonlinearity},
  year={2014},
  volume={27},
  pages={2419 - 2443}
}
We investigate determinantal point processes on [0, +∞) of the form We prove that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel–Darboux formula if , and that they can be characterized in terms of 1 × 2 vector-valued Riemann–Hilbert problems, which exhibit some non-standard properties. In addition, we obtain expressions for the equilibrium measure associated with our model if w(λ) = e−nV (λ) in the one-cut case with and without a hard… 

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