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A conditional limit theorem for high-dimensional ℓᵖ-spheres
- Source :
- Journal of Applied Probability. 55:1060-1077
- Publication Year :
- 2018
- Publisher :
- Cambridge University Press (CUP), 2018.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 55
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi...........7c887c1d7c43e66b48e4601d5af8e2df