Random walks on nilpotent groups driven by measures supported on powers of generators
| العنوان: | Random walks on nilpotent groups driven by measures supported on powers of generators |
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| المؤلفون: | Tianyi Zheng, Laurent Saloff-Coste |
| سنة النشر: | 2012 |
| مصطلحات موضوعية: | Group (mathematics), Probability (math.PR), 010102 general mathematics, Group Theory (math.GR), Central series, Random walk, 01 natural sciences, Measure (mathematics), Functional Analysis (math.FA), Combinatorics, Mathematics - Functional Analysis, 010104 statistics & probability, Nilpotent, FOS: Mathematics, Discrete Mathematics and Combinatorics, Interval (graph theory), Geometry and Topology, Finitely-generated abelian group, 0101 mathematics, Mathematics - Group Theory, Mathematics - Probability, Mathematics |
| الوصف: | We study the decay of convolution powers of a large family $\mu_{S,a}$ of measures on finitely generated nilpotent groups. Here, $S=(s_1,...,s_k)$ is a generating $k$-tuple of group elements and $a= (\alpha_1,...,\alpha_k)$ is a $k$-tuple of reals in the interval $(0,2)$. The symmetric measure $\mu_{S,a}$ is supported by $S^*=\{s_i^{m}, 1\le i\le k,\,m\in \mathbb Z\}$ and gives probability proportional to $$(1+m)^{-\alpha_i-1}$$ to $s_i^{\pm m}$, $i=1,...,k,$ $m\in \mathbb N$. We determine the behavior of the probability of return $\mu_{S,a}^{(n)}(e)$ as $n$ tends to infinity. This behavior depends in somewhat subtle ways on interactions between the $k$-tuple $a$ and the positions of the generators $s_i$ within the lower central series $G_{j}=[G_{j-1},G]$, $G_1=G$. |
| اللغة: | English |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::639e8df530d815308ed5b1758282248eTest http://arxiv.org/abs/1211.3003Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....639e8df530d815308ed5b1758282248e |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |