The Derrida-Retaux model on a geometric Galton-Watson tree
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915924717600768 |
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| author | Alsmeyer, Gerold Hu, Yueyun Mallein, Bastien |
| author_facet | Alsmeyer, Gerold Hu, Yueyun Mallein, Bastien |
| contents | We consider a generalized Derrida-Retaux model on a Galton-Watson tree with a geometric offspring distribution. For a class of recursive systems, including the Derrida-Retaux model with either a geometric or exponential initial distribution, we characterize the critical curve using an involution-type equation and prove that the free energy satisfies the Derrida-Retaux conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Derrida-Retaux model on a geometric Galton-Watson tree Alsmeyer, Gerold Hu, Yueyun Mallein, Bastien Probability 60J80, 82B27 We consider a generalized Derrida-Retaux model on a Galton-Watson tree with a geometric offspring distribution. For a class of recursive systems, including the Derrida-Retaux model with either a geometric or exponential initial distribution, we characterize the critical curve using an involution-type equation and prove that the free energy satisfies the Derrida-Retaux conjecture. |
| title | The Derrida-Retaux model on a geometric Galton-Watson tree |
| topic | Probability 60J80, 82B27 |
| url | https://arxiv.org/abs/2502.02991 |