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arXiv · 1409.2667

The asymptotic behaviour of the discrete holomorphic map $Z^a$ via the Riemann-Hilbert method

Alexander I. Bobenko·Alexander Its
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Abstract

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.

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Alexander I. Bobenko, Alexander Its. 2014-09-09. The asymptotic behaviour of the discrete holomorphic map $Z^a$ via the Riemann-Hilbert method. https://doi.org/10.1215/00127094-3620012

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