与仿射反射群相关的出口问题
Exit problems associated with affine reflection groups
摘要：
得到了布朗运动从仿射外尔群凹室的第一次出时的分布公式。在大多数情况下，该公式是表示compensation，在Pfweans。期望的退出时间在类型à case中导出。所得结果可推广到其它马尔可夫过程。我们还给出了公式的Dirichlet和Neumann Laplacian的凹室上的实本征函数，观察到的“热点”猜想的J.劳赫是真实的凹室。
英文摘要：
We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type à case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the `Hot Spots' conjecture of J. Rauch is true for alcoves.
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。
