Geometric Large-Deviation-Type Principles for Mixed Measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917290293854208 |
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| author | Lafi, Malak Zvavitch, Artem |
| author_facet | Lafi, Malak Zvavitch, Artem |
| contents | We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we prove a geometric large-deviation-type asymptotic for first-order mixed measures, where the decay under dilation is governed by a natural inradius associated with the measure. In the planar case, we derive an explicit integral representation for second-order mixed measures and obtain a corresponding asymptotic. As an application, we prove a comparison theorem showing that asymptotic dominance under dilation forces inclusion between convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18927 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Large-Deviation-Type Principles for Mixed Measures Lafi, Malak Zvavitch, Artem Probability Metric Geometry 52A20, 52A21, 46T12, 60F10 We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we prove a geometric large-deviation-type asymptotic for first-order mixed measures, where the decay under dilation is governed by a natural inradius associated with the measure. In the planar case, we derive an explicit integral representation for second-order mixed measures and obtain a corresponding asymptotic. As an application, we prove a comparison theorem showing that asymptotic dominance under dilation forces inclusion between convex bodies. |
| title | Geometric Large-Deviation-Type Principles for Mixed Measures |
| topic | Probability Metric Geometry 52A20, 52A21, 46T12, 60F10 |
| url | https://arxiv.org/abs/2602.18927 |