摘要

Let D be an invertible matrix and L1 (x) denote the well-known 1-norm of xRn. In this note we analyse the kth moment of the ratio L1 (D1z) and its asymptotics in special cases, where z is uniformly distributed over the unit hypersphere. Conceptually, L1 (D1z) can be seen as the (weighted) length, measured along fixed orientations, of a path connecting any two points relative to their straight line distance.

  • 出版日期2013-5