Electrostatics on Branching Processes
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916316469788672 |
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| author | Sinclair, Christopher D. |
| author_facet | Sinclair, Christopher D. |
| contents | We introduce a random probability measure on the profinite completion of the random tree of a branching process and introduce the canonical and grand canonical ensembles of random repelling particles on this random profinite completion at inverse temperature $β> 0$. We think of this as a random spatial process of particles in a random tree, and we introduce the notion of the {\em mean} canonical and grand canonical partition functions where in this context `mean' means averaged over the random environment. We give a recursion for these mean partition functions and demonstrate that in certain instances, determined by the law for the branching process, these partition functions as a function of $β$ have algebraic properties which generalize those that appear in the non-random and $p$-adic environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Electrostatics on Branching Processes Sinclair, Christopher D. Mathematical Physics Probability 15B52, 60B05, 60B20, 60G55, 60G57, 60J80, 60K37, 82B20, 82B23, 82B31 We introduce a random probability measure on the profinite completion of the random tree of a branching process and introduce the canonical and grand canonical ensembles of random repelling particles on this random profinite completion at inverse temperature $β> 0$. We think of this as a random spatial process of particles in a random tree, and we introduce the notion of the {\em mean} canonical and grand canonical partition functions where in this context `mean' means averaged over the random environment. We give a recursion for these mean partition functions and demonstrate that in certain instances, determined by the law for the branching process, these partition functions as a function of $β$ have algebraic properties which generalize those that appear in the non-random and $p$-adic environments. |
| title | Electrostatics on Branching Processes |
| topic | Mathematical Physics Probability 15B52, 60B05, 60B20, 60G55, 60G57, 60J80, 60K37, 82B20, 82B23, 82B31 |
| url | https://arxiv.org/abs/2407.06433 |