Speaker
Alexander Aptekarev
(Keldysh Institute RAS)
Description
Let $\mu(x):=(\mu_1(x),\dots , \mu_d(x))$ be a vector of positive measures. For a given multiindex $n=(n_1, \dots , n_d)$ we consider a polynomial $P_n(x)$ of degree $|n|:=n_1+ \cdots +n_p$, which satisfies $n_j$ orthogonality relations to the degrees of the scalar variable $x$ with respect to the measure $\mu_j$, $j=1, \dots , p$. Such polynomials always exist and they are called multiple orthogonal polynomials. For $p=1$ we have usual orthogonal polynomials. We discuss several examples of ensembles of random matrices related to the multiple orthogonal polynomials (namely: random matrix model with external source, two matrix model and normal matrix model). An application to the Brownian bridges will be highlighted.
Primary author
Alexander Aptekarev
(Keldysh Institute RAS)
