Limit theorems for the volumes of small codimensional random sections of \(\ell_{p}^{n}\)-balls

DOI10.1214/23-AOP1646arXiv2206.14311OpenAlexW4391363490MaRDI QIDQ6118755

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Publication date: 28 February 2024

Published in: (Search for Journal in Brave)

Abstract: We establish Central Limit Theorems for the volumes of intersections of

B_{p}^{n}

(the unit ball of

e l l_{p}^{n}

) with uniform random subspaces of codimension

d

for fixed

d

and

n o i n f t y

. As a corollary we obtain higher order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan--Klartag version of CLT for convex bodies. We also obtain a Central Limit Theorem for the Minkowski functional of the intersection body of

B_{p}^{n}

, evaluated on a random vector distributed uniformly on the unit sphere.

Full work available at URL: https://arxiv.org/abs/2206.14311

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