We study the asymptotic behavior of the discrete analogue of the holomorphic map . 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 formulas which were conjectured in 2000.
"The asymptotic behavior of the discrete holomorphic map via the Riemann–Hilbert method." Duke Math. J. 165 (14) 2607 - 2682, 1 October 2016. https://doi.org/10.1215/00127094-3620012