Biorthogonal ensembles with two-particle interactions
(2014) Nonlinearity — Vol. 27, n° 10, p. 2419-2443 (2014)
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- 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 $ hetainmathbb Q$ , 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 edge
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Claeys, T., & Romano, S. (2014). Biorthogonal ensembles with two-particle interactions. Nonlinearity, 27(10), 2419-2443. https://doi.org/10.1088/0951-7715/27/10/2419 (Original work published 2014)