论文标题
在对称空间上随机步行的局部极限定理
Local limit theorem for random walks on symmetric spaces
论文作者
论文摘要
我们降低了作用于其对称空间的非紧密锻炼半神经谎言组的局部极限定理，以确定与该度量相关的自然算子是准混合的。在对基础措施的强烈养分假设下，我们为所讨论的操作员推断出必要的光谱结果。因此，我们给出了满足这种局部限制定理的有限支持措施的第一个例子。此外，在其他假设下证明了本地限制定理的定量错误率。
We reduce the local limit theorem for a non-compact semisimple Lie group acting on its symmetric space to establishing that a natural operator associated to the measure is quasicompact. Under strong Diophantine assumptions on the underlying measure, we deduce the necessary spectral results for the operator in question. We thereby give the first examples of finitely supported measures satisfying such a local limit theorem. Moreover, quantitative error rates for the local limit theorem are proved under additional assumptions.
