The asymptotic behavior of the discrete holomorphic map Za via the Riemann–Hilbert method

Alexander I. Bobenko; Alexander Its

doi:10.1215/00127094-3620012

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 formulas which were conjectured in 2000.

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Alexander I. Bobenko. Alexander Its. "The asymptotic behavior of the discrete holomorphic map $Z^{a}$ via the Riemann–Hilbert method." Duke Math. J. 165 (14) 2607 - 2682, 1 October 2016. https://doi.org/10.1215/00127094-3620012

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Received: 10 September 2014; Revised: 30 October 2015; Published: 1 October 2016

First available in Project Euclid: 13 July 2016

zbMATH: 1354.30041

MathSciNet: MR3551770

Digital Object Identifier: 10.1215/00127094-3620012

Subjects:

Primary: 52C26

Secondary: 35Q15 , 39A12

Keywords: discrete complex analysis , discrete differential geometry , discrete integrable systems , Riemann–Hilbert problem

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