论文标题
绝对连续的Furstenberg措施有限地支持随机步行
Absolutely continuous Furstenberg measures for finitely-supported random walks
论文作者
论文摘要
在本说明中，我们概括了一般性支持的对称措施的构造，其furstenberg措施的密度从$ \ mathrm {Slrm {sl} _2（\ Mathbb {r}）$到一个普通简单的Lie Group的情况平滑。证明与波尔加因相同，只是在最大紧凑型亚组上使用谐波分析替代了傅立叶系列。
In this note, we generalise a Bourgain's construction of finitely-supported symmetric measures whose Furstenberg measure has a smooth density from the case of $\mathrm{SL}_2(\mathbb{R})$ to that of a general simple Lie group. The proof is the same as Bourgain's, except that the use of Fourier series is replaced by harmonic analysis on a maximal compact subgroup.
