Title: Asymptotic count of edge-bicolored graphs
| Speaker | Michael Borinsky |
| Affiliation | Perimeter Institute and C&O |
| Location | MC 5479 |
Abstract: I will talk about recent joint work with Chiara Meroni and Max Wiesmann, where we showed 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. An interesting application of this purely combinatorial work to mathematical physics is the Ising model on a random graph. I will explain how its phase transitions arise from our formula.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,