论文标题
在通用线性组上随机行走系数的中等偏差和局部极限定理
Moderate deviations and local limit theorems for the coefficients of random walks on the general linear group
论文作者
论文摘要
考虑随机步行$ g_n：= g_n \ ldots g_1 $，$ n \ geq 1 $，其中$（g_n）_ {n \ geq 1} $是一系列独立且相同分布的随机元素，该元素与law $μ$ $ $ $ $ $ $ $ $ {在$μ$的适当条件下，我们建立了cramér型中等偏差扩展和本地限制定理，其系数$ \ langle f，g_n v \ rangle $，其中$ v \ in v $ in v $ and $ f \ in v^*$。我们的方法是基于马尔可夫链$ g_n \！\ cdot \！的不变度度量的Hölder规律性。 X = \ Mathbb r g_n V $在$ V $的投影空间上，起点$ x = \ Mathbb r V $，在更改的度量下。
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.
