Report
Local limits of random spanning trees in random environment
| العنوان: | Local limits of random spanning trees in random environment |
|---|---|
| المؤلفون: | Makowiec, Luca |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Combinatorics, 60K35 (Primary) 82B41, 82B44, 05C05 (Secondary) |
| الوصف: | We study the edge overlap and local limit of the random spanning tree in random environment (RSTRE) on the complete graph with $n$ vertices and weights given by $\exp(-\beta \omega_e)$ for $\omega_e$ uniformly distributed on $[0,1]$. We show that for $\beta$ growing with $\beta = o(n/\log n)$, the edge overlap is $(1+o(1)) \beta$, while for $\beta$ much larger than $n \log^2 n$, the edge overlap is $(1-o(1))n$. Furthermore, there is a transition of the local limit around $\beta = n$. When $\beta = o(n/ \log n)$ the RSTRE locally converges to the same limit as the uniform spanning tree, whereas for $\beta$ larger than $n \log^\lambda n$, where $\lambda = \lambda(n) \rightarrow \infty$ arbitrarily slowly, the local limit of the RSTRE is the same as that of the minimum spanning tree. Comment: 19 pages, Comments are welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2410.16836 |
| رقم الانضمام: | edsarx.2410.16836 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |