由路的Wiener测度诱导的凸曲面的局部测度
Local Measure of Convex Surfaces induced by the Wiener Measure of Paths
摘要:
维纳测度是一个闭的、凸的、(d-1)维的欧氏(超)曲面的测度,它是闭的d维布朗桥的凸包。我提出的参数和数值证据表明,这一措施,奇数d,是由一个本地的经典行动的长度尺寸两个依赖于几何不变的(d-1)维表面只产生。
英文摘要:
The Wiener measure induces a measure of closed, convex, (d-1)-dimensional, Euclidean (hyper-)surfaces that are the convex hulls of closed d-dimensional Brownian bridges. I present arguments and numerical evidence that this measure, for odd d, is generated by a local classical action of length dimension two that depends on geometric invariants of the (d-1)-dimensional surface only.
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