تقرير
Electrostatics on Branching Processes
| العنوان: | Electrostatics on Branching Processes |
|---|---|
| المؤلفون: | Sinclair, Christopher D. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Probability, 15B52, 60B05, 60B20, 60G55, 60G57, 60J80, 60K37, 82B20, 82B23, 82B31 |
| الوصف: | 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 $\beta > 0$. 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 $\beta$ have algebraic properties which generalize those that appear in the non-random and $p$-adic environments. Comment: 13 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06433 |
| رقم الأكسشن: | edsarx.2407.06433 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |