TY - JOUR
T1 - Estimate of observable diameter of l p-product spaces
AU - Ozawa, Ryunosuke
AU - Shioya, Takashi
N1 - Funding Information:
The authors are partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science. The first author is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2015/7/27
Y1 - 2015/7/27
N2 - We estimate the observable diameter of the lp-product space Xn of an mm-space X by using the limit formula in our previous paper (Ozawa and Shioya, Math. Zeit. (to appear)). The idea of our proof is based on Gromov’s book (In: Metric structures for Riemannian and non-Riemannian spaces, 2007). As a corollary we obtain the phase transition property of {Xn}n=1∞ under a uniform discreteness condition.
AB - We estimate the observable diameter of the lp-product space Xn of an mm-space X by using the limit formula in our previous paper (Ozawa and Shioya, Math. Zeit. (to appear)). The idea of our proof is based on Gromov’s book (In: Metric structures for Riemannian and non-Riemannian spaces, 2007). As a corollary we obtain the phase transition property of {Xn}n=1∞ under a uniform discreteness condition.
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U2 - 10.1007/s00229-015-0730-1
DO - 10.1007/s00229-015-0730-1
M3 - Article
AN - SCOPUS:84933177371
SN - 0025-2611
VL - 147
SP - 501
EP - 509
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3-4
ER -