A conditional limit theorem for high-dimensional ℓᵖ-spheres
| Autor: | Kavita Ramanan, Steven Soojin Kim |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Pure mathematics Kullback–Leibler divergence Convex geometry Euclidean space General Mathematics Convex set 01 natural sciences 010101 applied mathematics 010104 statistics & probability Probability theory Limit (mathematics) 0101 mathematics Statistics Probability and Uncertainty Rate function Event (probability theory) Mathematics |
| Zdroj: | Journal of Applied Probability. 55:1060-1077 |
| ISSN: | 1475-6072 0021-9002 |
| Popis: | The study of high-dimensional distributions is of interest in probability theory, statistics, and asymptotic convex geometry, where the object of interest is the uniform distribution on a convex set in high dimensions. The ℓp-spaces and norms are of particular interest in this setting. In this paper we establish a limit theorem for distributions on ℓp-spheres, conditioned on a rare event, in a high-dimensional geometric setting. As part of our proof, we establish a certain large deviation principle that is also relevant to the study of the tail behavior of random projections of ℓp-balls in a high-dimensional Euclidean space. |
| Databáze: | OpenAIRE |
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