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1 October 2016 The asymptotic behavior of the discrete holomorphic map Za via the Riemann–Hilbert method
Alexander I. Bobenko, Alexander Its
Duke Math. J. 165(14): 2607-2682 (1 October 2016). DOI: 10.1215/00127094-3620012

Abstract

We study the asymptotic behavior of the discrete analogue of the holomorphic map za. 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.

Citation

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

Information

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

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 14 • 1 October 2016
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