Report
Local law and Tracy--Widom limit for sparse stochastic block models
| العنوان: | Local law and Tracy--Widom limit for sparse stochastic block models |
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| المؤلفون: | Hwang, Jong Yun, Lee, Ji Oon, Yang, Wooseok |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 60B20, 15B52, 05C80 |
| الوصف: | We consider the spectral properties of sparse stochastic block models, where $N$ vertices are partitioned into $K$ balanced communities. Under an assumption that the intra-community probability and inter-community probability are of similar order, we prove a local semicircle law up to the spectral edges, with an explicit formula on the deterministic shift of the spectral edge. We also prove that the fluctuation of the extremal eigenvalues is given by the GOE Tracy--Widom law after rescaling and centering the entries of sparse stochastic block models. Applying the result to sparse stochastic block models, we rigorously prove that there is a large gap between the outliers and the spectral edge without centering. Comment: 68 pages. 2 Figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1903.02179 |
| رقم الانضمام: | edsarx.1903.02179 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |