Abstract
In this paper, we prove a Sanov-type large deviation principle for the sequence of empirical measures of vectors chosen uniformly at random from an Orlicz ball. From this level-2 large deviation result, in a combination with Gibbs conditioning, entropy maximization and an Orlicz version of the Poincaré-Maxwell-Borel lemma, we deduce a conditional limit theorem for high-dimensional Orlicz balls. In more geometric parlance, the latter shows that if V1 and V2 are Orlicz functions, then random points in the V1-Orlicz ball, conditioned on having a small V2-Orlicz radius, look like an appropriately scaled V2-Orlicz ball. In fact, we show that the limiting distribution in our Poincaré-Maxwell-Borel lemma, and thus the geometric interpretation, undergoes a phase transition depending on the magnitude of the V2-Orlicz radius.
Original language | English |
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Article number | 128169 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 536 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Aug 2024 |
Keywords
- Entropy maximization
- Gibbs conditioning principle
- Large deviation principle
- Orlicz space
- Poincaré-Maxwell-Borel lemma
- Sanov's theorem
ASJC Scopus subject areas
- Analysis
- Applied Mathematics