| Autor: |
Chen, Zhen-Qing, Kumagai, Takashi, Saloff-Coste, Laurent, Wang, Jian, Zheng, Tianyi |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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