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arXiv · 1402.6831

Limit formulas for metric measure invariants and phase transition property

Ryunosuke Ozawa·Takashi Shioya
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Abstract

We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition property for a sequence of metric measure spaces or pyramids, and find some examples of symmetric spaces of noncompact type with the phase transition property. We also give a simple proof of a theorem by Funano-Shioya on the limit of an $N$-L\'evy family.

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Ryunosuke Ozawa, Takashi Shioya. 2014-02-27. Limit formulas for metric measure invariants and phase transition property. https://arxiv.org/abs/1402.6831

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