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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.17976 |
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Table of Contents:
- This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in the Prokhorov -- Le Cam theorem. The proof only uses elementary tools from probability theory. Sequential tightness gives means to characterize the precompact collections of random curves on a compact geodesic metric space in terms of an annulus crossing condition, which generalizes the one by Aizenman and Burchard by allowing estimates for annulus crossing probabilities to be non-uniform over the modulus of annuli.