Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Let $F=\{g_t\}$ be a one-parametr diagonal subgroup of $SL_n(\mathbb R)$.
We assume $F$ has no nonzero invariant vectors in $\mathbb R^n$.
Let $x\in X, \varphi\in C_c(X)$ and $\mu$ be the probability Haar measure
on $X$. For certain proper subgroup $U$ of the unstable horospherical subgroup
of $g_1$ we show that for almost every $u\in U$
\[
\frac{1}{T}\int_0^T\varphi({g_tux})dt \to \int_X\varphi d\mu.
\]
If $\varphi$ is moreover smooth, we can get an error rate of the convergence.
The error rate is ineffective due to the use of Borel-Cantelli lemma.