arXiv Open Access 2022

Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group

Hui Xiao Ion Grama Quansheng Liu

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Abstrak

Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $μ$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$. Under suitable conditions on $μ$, we establish Cramér type moderate deviation expansions and local limit theorems with moderate deviations for the coefficients $\langle f, G_n v \rangle$, where $v \in V$ and $f \in V^*$. Our approach is based on the Hölder regularity of the invariant measure of the Markov chain $G_n \!\cdot \! x = \mathbb R G_n v$ on the projective space of $V$ with the starting point $x = \mathbb R v$, under the changed measure.

Topik & Kata Kunci

math.PR math.GR

Penulis (3)

Hui Xiao

Ion Grama

Quansheng Liu

Format Sitasi

APA MLA BibTeX

Xiao, H., Grama, I., Liu, Q. (2022). Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group. https://arxiv.org/abs/2209.04628

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Informasi Jurnal

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