Seminar
From Gumbel to Tracy-Widom II, via integer partitions
by Quinten Van Baelen (KU Leuven)
Location: 200B.02.18, Leuven
Time: Wednesday May 22, 2019 at
16:00
We investigate the zeros of discrete orthogonal polynomials on the q-lattice \(q^k, k=0,1,2,3, …,\) where \(0 < q < 1.\) The zeros accumulate asymptotically on this q-lattice, which itself has an accumulation point at 0. In order to avoid this accumulation at 0 we will take the nth roots of the zeros of \(p_n\) and investigate the zeros of \(p_n(x^n)\ \) as \(\ n \to \infty\). This is done using an equilibrium problem in logarithmic potential theory with a constraint, where the constraint is given by the asymptotic distribution of the points in the q-lattice, after taking the \(n\)th root.
