In this excellent paper the authors study asymptotics for orthogonal polynomials with respect to the weights
on the real line, with an even polynomial of degree with positive leading coefficients
The main results cover
a. asymptotics for the leading and recurrence coefficients (Theorem 2.1),
b. Plancherel-Rotach asymptotics on the whole complex plane (Theorem 2.2),
c. asymptotic location of the zeros (Theorem 2.3).
The deep results are derived through recently developed methods and a reformulation as a Riemann-Hilbert problem due to A. S. Fokas, A. R. Its and A. V. Kitaev [Commun. Math. Phys. 142, 313-344 (1991; Zbl 0742.35047); ibid. 147, 395-430 (1992; Zbl 0760.35051)].
The solution of this Riemann-Hilbert problem is then subjected to a series of transformations, leading to deep asymptotic results.
The technical and delicate operations are described in detail and give the reader a good insight in the different techniques needed. In view of the intricacies of the methods, the length of the paper is just about right.