On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

Abstract: We consider multiple orthogonal polynomials with respect to Nikishin systems generated by two measures $(\sigma_1, \sigma_2)$ with unbounded supports ($\mbox{supp} \, \sigma_1 \subseteq \mathbb{R}+$, $\mbox{supp} \, \sigma_2 \subseteq \,\mathbb{R}-$) and $\sigma_2$ is discrete. A Nikishin type equilibrium problem in the presence of an external field acting on $\mathbb{R}+$ and a constraint on $ \mathbb{R}-$ is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.