English

A note on invariance of the Cauchy and related distributions

Probability 2019-09-24 v2 Complex Variables

Abstract

It is known that if ff is an analytic self map of the complex upper half-plane which also maps R{}\mathbb{R}\cup\{\infty\} to itself, and f(i)=if(i)=i, then ff preserves the Cauchy distribution. This note concerns three results related to the above fact.

Keywords

Cite

@article{arxiv.1908.04006,
  title  = {A note on invariance of the Cauchy and related distributions},
  author = {Wooyoung Chin and Paul Jung and Greg Markowsky},
  journal= {arXiv preprint arXiv:1908.04006},
  year   = {2019}
}