Bivariate exponential integrals and edge-bicolored graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908384534462464 |
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| author | Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian |
| author_facet | Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bivariate exponential integrals and edge-bicolored graphs Borinsky, Michael Meroni, Chiara Wiesmann, Maximilian Combinatorics Mathematical Physics 05C30, 41A60 (Primary) 05A15, 32A55, 82B26 (Secondary) 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. |
| title | Bivariate exponential integrals and edge-bicolored graphs |
| topic | Combinatorics Mathematical Physics 05C30, 41A60 (Primary) 05A15, 32A55, 82B26 (Secondary) |
| url | https://arxiv.org/abs/2409.18607 |