A conditional limit theorem for high-dimensional ℓᵖ-spheres

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.

• Publication year

  2018

• Venue

  Journal of Applied Probability

• Publication date

  2018-12-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1017/jpr.2018.71
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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