PIRSA:25050033 Scientific Series Mathematical physics

DOI10.48660/25050033

Series: Mathematical Physics

Wiesmann, M. (2025). Edge-colored graphs and exponential integrals. Perimeter Institute. https://pirsa.org/25050033

Wiesmann, Maximilian. Edge-colored graphs and exponential integrals. Perimeter Institute, May. 15, 2025, https://pirsa.org/25050033 

@misc{ pirsa_PIRSA:25050033,
  doi = {10.48660/25050033},
  url = {https://pirsa.org/25050033},
  author = {Wiesmann, Maximilian},
  keywords = {Mathematical physics},
  language = {en},
  title = {Edge-colored graphs and exponential integrals},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {may},
  note = {PIRSA:25050033 see, \url{https://pirsa.org}}
}

Abstract

We show that specific exponential integrals serve as generating functions of labeled edge-colored graphs. Based on this, we derive asymptotics for the number of edge-colored 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 graph and show how its phase transitions arise from our formula.

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