Estimate of observable diameter of $l_p$-product spaces

Abstract

We estimate the observable diameter of the $l_p$-product space $X^n$ of an mm-space $X$ by using the limit formula in our previous paper. The idea of our proof is based on Gromov's book. As a corollary we obtain the phase transition property of $\{X^n{\}}_{n=1}^{\infty }$ under a discreteness condition.

10 pages