论文标题
紧凑型谎言群体随机元素的力量的渐近学
Asymptotics of powers of random elements of compact Lie groups
论文作者
论文摘要
对于一个紧凑的Lie Group \（l \）的Haar分配的元素$ H $，Eric Rains证明，有一个自然的数字$ d = d_l $，因此，对于所有$ d \ ge d $，$ h^d $的特征分布是固定的，并且降低了这一固定的eigenvalue分发。在本文中，我们考虑一个随机元素$ u u $ $ u $的紧凑型谎言组，具有一般分布。特别是，我们引入了一种轻度的绝对连续性条件，在该条件下，$ u $ $ u $的权力的特征值分布将$ h^d $的特征分布收集到$ h^d $。然后，我们考虑$ u^d $本身的限制分布而不是特征值分布。
For a Haar-distributed element $H$ of a compact Lie group \(L\), Eric Rains proved that there is a natural number $D = D_L$ such that, for all $d\ge D$, the eigenvalue distribution of $H^d$ is fixed, and Rains described this fixed eigenvalue distribution explicitly. In the present paper we consider random elements $U$ of a compact Lie group with general distribution. In particular, we introduce a mild absolute continuity condition under which the eigenvalue distribution of powers of $U$ converges to that of $H^D$. Then, rather than the eigenvalue distribution, we consider the limiting distribution of $U^d$ itself.
