تقرير
Concatenating Random Matchings
| العنوان: | Concatenating Random Matchings |
|---|---|
| المؤلفون: | Burghart, Fabian, Thévenin, Paul |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Combinatorics, 60C05 (Primary), 05C30 (Secondary) |
| الوصف: | We consider the concatenation of $t$ uniformly random perfect matchings on $2n$ vertices, where the operation of concatenation is inspired by the multiplication of generators of the Brauer algebra $\mathfrak{B}_n(\delta)$. For the resulting random string diagram $\mathsf{Br}_n(t)$, we observe a giant component if and only if $n$ is odd, and as $t\to\infty$ we obtain asymptotic results concerning the number of loops, the size of the giant component, and the number of loops of a given shape. Moreover, we give a local description of the giant component. These results mainly rely on the use of renewal theory and the coding of connected components of $\mathsf{Br}_n(t)$ by random vertex-exploration processes. Comment: 30 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.11596 |
| رقم الأكسشن: | edsarx.2306.11596 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |