تقرير
Limit theorems for some long range random walks on torsion free nilpotent groups
العنوان: | Limit theorems for some long range random walks on torsion free nilpotent groups |
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المؤلفون: | Chen, Zhen-Qing, Kumagai, Takashi, Saloff-Coste, Laurent, Wang, Jian, Zheng, Tianyi |
سنة النشر: | 2022 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Group Theory, Primary 60G50, 60G51, 20F65, 60B15, Secondary 60J46, 60J45 |
الوصف: | We consider a natural class of long range random walks on torsion free nilpotent groups and develop limit theorems for these walks. Given the original discrete group $\Gamma$ and a random walk $(S_n)_ {n\ge1}$ driven by a certain type of symmetric probability measure $\mu$, we construct a homogeneous nilpotent Lie group $G_\bullet(\Gamma,\mu)$ which carries an adapted dilation structure and a stable-like process $(X_t)_{ t\ge0}$ which appears in a Donsker-type functional limit theorem as the limit of a rescaled version of the random walk. Both the limit group and the limit process on that group depend on the measure $\mu$. In addition, the functional limit theorem is complemented by a local limit theorem. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2207.11371 |
رقم الأكسشن: | edsarx.2207.11371 |
قاعدة البيانات: | arXiv |
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