论文标题
Edgeworth的扩展，用于一般线性群的随机步行系数
Edgeworth expansion for the coefficients of random walks on the general linear group
论文作者
论文摘要
令$（g_n）_ {n \ geq 1} $为一系列独立且相同分布的随机元素，其中$ $ $ $ $ $ $ $ $ $ $ $ $ \ textUp {gl}（v）$，其中$ v = \ mathbb r^d $。考虑随机步行$ g_n：= g_n \ ldots g_1 $，$ n \ geq 1 $。在$μ$的适当条件下，我们建立了系数的一阶Edgeworth扩展，$ \ langle f，g_n v \ rangle $，$ v \ in V $中的$ v \ in v $ in v $ in v^*$中，与vector norm norm $ \ | g_n v \ | $相比，出现了新的额外术语。
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 $\|G_n v\|$.
