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Edgeworth expansion for the coefficients of random walks on the general linear group
- Publication Year :
- 2022
-
Abstract
- Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random elements with law $\mu$ 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 $\mu$, 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 $\|G_n v\|$.<br />Comment: This paper is a part of the results which previously appeared in Xiao, Grama, Liu "Limit theorems for the coefficients of random walks on the general linear group" arXiv:2111.10569, 2021
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2209.03623
- Document Type :
- Working Paper