无限测度下对称随机游动的瞬变律
Transience in law for symmetric random walks in infinite measure
摘要：
本文考虑了第二可数局部紧拓扑空间上的随机游动，并赋予其不变的Radon测度.我们表明，如果步行是对称的，如果每一个子集是不变的步行有零或无限的措施，那么一个逃逸的质量几乎每一个起点。然后，我们将这一结果的上下文中的齐次随机游动无限体积空间，并推出一个逆Eskin-Margulis递归定理。
英文摘要：
We consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset which is invariant by the walk has zero or infinite measure, then one has escape of mass for almost every starting point. We then apply this result in the context of homogeneous random walks on infinite volume spaces, and deduce a converse to Eskin-Margulis recurrence theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
