The asymptotic behaviour of the discrete holomorphic map $Z^a$ via the   Riemann-Hilbert method
  We study the asymptotic behavior of the discrete analogue of the holomorphic map $z^a$. The analysis is based on the use of the Riemann-Hilbert approach. Specifically, using the Deift-Zhou nonlinear steepest descent method we prove the asymptotic formulae which was conjectured in 2000 by the first co-author and S.I.~Agafonov. 
Alexander I. Bobenko, Alexander Its
math.CV nlin.SI