PIRSA:25050033

Edge-colored graphs and exponential integrals

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}}
          }

Maximilian Wiesmann Max Planck Institute for Mathematics in the Sciences

Talk numberPIRSA:25050033
DOI10.48660/25050033
Collection
Talk Type Scientific Series
Subject

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.