A central limit theorem in the framework of the Thompson group $F$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909323616059392 |
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| author | Krishnan, Arundhathi |
| author_facet | Krishnan, Arundhathi |
| contents | We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. We consider the sequence of self-adjoint elements given by $a_n=\frac{g_n+g_n^{*}}{\sqrt{2}}$ in the noncommutative probability space $(\mathbb{C}(F),φ)$, where the expectation functional $φ$ is the trace associated to the left regular representation of $F$, and the $g_n$-s are the generators of $F$ in its standard infinite presentation. We show that the limit law of the sequence $s_n = \frac{a_0+\cdots+a_{n-1}}{\sqrt{n}}$ is the standard normal distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05626 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A central limit theorem in the framework of the Thompson group $F$ Krishnan, Arundhathi Operator Algebras Combinatorics Group Theory Probability Primary: 46L53, 60F05, Secondary: 05E16, 20M05, 68Q42, 68R15 We discuss a central limit theorem in the framework of the group algebra of the Thompson group $F$. We consider the sequence of self-adjoint elements given by $a_n=\frac{g_n+g_n^{*}}{\sqrt{2}}$ in the noncommutative probability space $(\mathbb{C}(F),φ)$, where the expectation functional $φ$ is the trace associated to the left regular representation of $F$, and the $g_n$-s are the generators of $F$ in its standard infinite presentation. We show that the limit law of the sequence $s_n = \frac{a_0+\cdots+a_{n-1}}{\sqrt{n}}$ is the standard normal distribution. |
| title | A central limit theorem in the framework of the Thompson group $F$ |
| topic | Operator Algebras Combinatorics Group Theory Probability Primary: 46L53, 60F05, Secondary: 05E16, 20M05, 68Q42, 68R15 |
| url | https://arxiv.org/abs/2309.05626 |