Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials (Q259100)

The Jacobi-Piñeiro and multiple Laguerre polynomials of the first kind are two families of multiple orthogonal polynomials useful for investigating certain aspects concerning the Bethe Ansatz equations, determinantal point processes and random matrix minor processes related to percolation theory. Using a result on the asymptotic behavior of the ratio of two neighboring polynomials, the authors obtain the asymptotic distribution of the zeros of these multiple orthogonal polynomials. Their result can be regarded as an extension to the multiple orthogonal polynomials of the equidistribution result for zeros of the orthogonal polynomials. The obtained asymptotic zero distributions are related to the Fuss-Catalan distribution.