Spheres and Minima
Probability
2016-09-07 v1 Classical Analysis and ODEs
Abstract
We write down a one-dimensional integral formula and compute large-n asymptotics for the expectation of the absolute value of the smallest component of a unit vector in n-dimensional Euclidean space. The method is general, and allows to write the mean over the sphere of an homogeneous function in terms of an expectation of a function of independent, identically distributed Gaussians. We also write down an asymptotic formula for the minimum of a large number of identical independent positive random variables.
Keywords
Cite
@article{arxiv.math/0305252,
title = {Spheres and Minima},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/0305252},
year = {2016}
}