We consider orthogonal polynomials pne−2nQn ,x for varying measures and use universality limits to prove ”local limits” limn→∞[Formula presented]e−[Formula presented]z=cosπz.Here yjn is a local maximum point of pne−nQn in the ”bulk” of the support, K̃nyjn,yjn is the normalized reproducing kernel, and the limit holds uniformly for z in compact subsets of the plane. We also consider local limits at the ”soft edge” of the spectrum, which involve the Airy function.
Bibliographical noteFunding Information:
Research supported by NSF grant DMS1800251.
© 2020 Elsevier Inc.
- Exponential weights
- Orthogonal Polynomials
- University Limits
- Varying Weights