Bivariate exponential integrals and edge-bicolored graphs
Combinatorics
2025-06-02 v1 Mathematical Physics
math.MP
Abstract
We show that specific exponential bivariate integrals serve as generating functions of labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the number of regular edge-bicolored graphs with arbitrary weights assigned to different vertex structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random 4-regular graph and show how its phase transitions arise from our formula.
Cite
@article{arxiv.2409.18607,
title = {Bivariate exponential integrals and edge-bicolored graphs},
author = {Michael Borinsky and Chiara Meroni and Maximilian Wiesmann},
journal= {arXiv preprint arXiv:2409.18607},
year = {2025}
}
Comments
20 pages, 5 figures. Comments are welcome!