# Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials, II

## TL;DR

This paper extends the analysis of ratio asymptotics for multiple orthogonal polynomials associated with Nikishin systems on star-like sets, expressing their limits via conformal mappings on Riemann surfaces.

## Contribution

It provides explicit descriptions of the limiting functions and recurrence coefficients in terms of conformal mappings, advancing understanding of Nikishin systems on star-like sets.

## Key findings

- Limiting functions expressed via conformal mappings on Riemann surfaces
- Recurrence coefficients are strictly positive and depend on support locations
- Detailed description of ratio asymptotics for multiple orthogonal polynomials

## Abstract

In this paper we continue the investigations initiated in \cite{LopLopstar} on ratio asymptotics of multiple orthogonal polynomials and functions of the second kind associated with Nikishin systems on star-like sets. We describe in detail the limiting functions found in \cite{LopLopstar}, expressing them in terms of certain conformal mappings defined on a compact Riemann surface of genus zero. We also express the limiting values of the recurrence coefficients, which are shown to be strictly positive, in terms of certain values of the conformal mappings. As a consequence, the limits depend exclusively on the location of the intervals determined by the supports of the measures that generate the Nikishin system.