Centers of probability measures without the mean

Giovanni Puccetti, Pietro Rigo, Bin Wang, Ruodu Wang

Published 2017-04-09Version 1

We investigate the set of centers of completely and jointly mixable distributions. In addition to several results, we show that, for each $n \geq 2$, there exist $n$ standard Cauchy random variables adding up to a constant $C$ if and only if $$|C|\le\frac{n\,\log (n-1)}{\pi}.$$