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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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| _version_ | 1866914163819806720 |
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| author | Abuzaid, Osama |
| author_facet | Abuzaid, Osama |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Precompactness of sequences of random variables and random curves revisited Abuzaid, Osama Probability 60B10 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. |
| title | Precompactness of sequences of random variables and random curves revisited |
| topic | Probability 60B10 |
| url | https://arxiv.org/abs/2505.17976 |