تقرير
A model for horizontally restricted random square-tiled surfaces
| العنوان: | A model for horizontally restricted random square-tiled surfaces |
|---|---|
| المؤلفون: | Fitzhugh, Nick, Schondorf, Aaron, Shrestha, Sunrose, Fallon, Sebastian Vander Ploeg, Zeng, Thomas |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Probability |
| الوصف: | A square-tiled surface (STS) is a (finite, possibly branched) cover of the standard square-torus with possible branching over exactly 1 point. Alternately, STSs can be viewed as finitely many axis-parallel squares with sides glued in parallel pairs. After a labelling of the squares by $\{1, \dots, n\}$, we can describe an STS with $n$ squares using two permutations $\sigma, \tau \in S_n$, where $\sigma$ encodes how the squares are glued horizontally and $\tau$ encodes how the squares are glued vertically. Hence, a previously considered natural model for STSs with $n$ squares is $S_n \times S_n$ with the uniform distribution. We modify this model to obtain a new one: We fix $\alpha \in [0,1]$ and let $\mathcal{K}_\mu$ be a conjugacy class of $S_n$ with at most $n^\alpha$ cycles. Then $\mathcal{K}_\mu \times S_n$ with the uniform distribution is a model for STSs with restricted horizontal gluings. We deduce the asymptotic (as $n$ grows) number of components, genus distribution, most likely stratum and set of holonomy vectors of saddle connections for random STSs in this new model. Comment: 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.14041 |
| رقم الأكسشن: | edsarx.2408.14041 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |