Universality Under Szegő's Condition
Printed: Mar 2016
This paper presents a
theorem on universality on orthogonal polynomials/random matrices
under a weak local condition on the weight function $w$.
With a new inequality for
polynomials and with the use of fast decreasing polynomials,
it is shown that an approach of
D. S. Lubinsky is applicable. The proof works
at all points which are Lebesgue-points both
for the weight function $w$ and for $\log w$.
universality, random matrices, Christoffel functions, asymptotics, potential theory
42C05 - Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
30C85 - Capacity and harmonic measure in the complex plane [See also 31A15]
31A15 - Potentials and capacity, harmonic measure, extremal length [See also 30C85]