Edge-colored graphs and exponential integralsConfirmed

by Maximilian Wiesmann (Max Planck Institute for Mathematics in the Sciences)

Thursday May 15, 2025, 11:00 AM → 12:30 PM America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

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.