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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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 $\|G_n v\|$.
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Dates et versions

hal-04541941 , version 1 (11-04-2024)

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Hui Xiao, Ion Grama, Quansheng Liu. Edgeworth expansion for the coefficients of random walks on the general linear group. 2024. ⟨hal-04541941⟩
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