Discrete period matrices and related topics

Abstract

We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a refining sequence of critical maps, the discrete period matrix converges to the continuous one.

35 pages; uses youngtab (provided). Fix some bugs, add comments and examples

References in corpus (3)

• Integrable systems on quad-graphs
• Dimers and the Critical Ising Model on Lattices of genus>1
• Discrete Polynomials and Discrete Holomorphic Approximation

Cited by in corpus (7)

• Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings
• New definitions of exponential, hyperbolic and trigonometric functions on time scales
• Geometric Structures on the Cochains of a Manifold
• Discrete Polynomials and Discrete Holomorphic Approximation
• Discrete Riemann surfaces based on quadrilateral cellular decompositions
• Exponentials form a basis of discrete holomorphic functions
• Discrete surfaces with length and area and minimal fillings of the circle