Duke Mathematical Journal

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

Alexander I. Bobenko and Alexander Its

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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.

Article information

Source
Duke Math. J., Volume 165, Number 14 (2016), 2607-2682.

Dates
Received: 10 September 2014
Revised: 30 October 2015
First available in Project Euclid: 13 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1468414744

Digital Object Identifier
doi:10.1215/00127094-3620012

Mathematical Reviews number (MathSciNet)
MR3551770

Zentralblatt MATH identifier
1354.30041

Subjects
Primary: 52C26: Circle packings and discrete conformal geometry
Secondary: 39A12: Discrete version of topics in analysis 35Q15: Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]

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

Citation

Bobenko, Alexander I.; Its, Alexander. The asymptotic behavior of the discrete holomorphic map $Z^{a}$ via the Riemann–Hilbert method. Duke Math. J. 165 (2016), no. 14, 2607--2682. doi:10.1215/00127094-3620012. https://projecteuclid.org/euclid.dmj/1468414744


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