Asymptotic zero distribution of some multiple orthogonal polynomials

Analysis Seminar
Monday, February 22, 2016 - 2:05pm
1 hour (actually 50 minutes)
Skiles 005
University of Leuven, Belgium
The asymptotic distribution of the zeros of two families of multiple orthogonal polynomials will be given, namely the Jacobi-Pineiro polynomials (which are an extension of the Jacobi polynomials) and the multiple Laguerre polynomials of the first kind (which are an extension of the Laguerre polynomials). We use the nearest neighbor recurrence relations for these polynomials and a recent result on the ratio asymptotics of multiple orthogonal polynomials. We show how these asymptotic zero distributions are related to the Fuss-Catalan distribution.