arXiv Open Access 2022

Edgeworth expansion for the coefficients of random walks on the general linear group

Hui Xiao Ion Grama Quansheng Liu

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Abstrak

Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random elements with law $μ$ on the general linear group $\textup{GL}(V)$, where $V=\mathbb R^d$. Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$. Under suitable conditions on $μ$, we establish the first-order Edgeworth expansion for the coefficients $\langle f, G_n v \rangle$ with $v \in V$ and $f \in V^*$, in which a new additional term appears compared to the case of vector norm $\|G_n v\|$.

Topik & Kata Kunci

math.PR

Penulis (3)

Hui Xiao

Ion Grama

Quansheng Liu

Format Sitasi

APA MLA BibTeX

Xiao, H., Grama, I., Liu, Q. (2022). Edgeworth expansion for the coefficients of random walks on the general linear group. https://arxiv.org/abs/2209.03623

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓