Comment on "Sum of squares of uniform random variables" by I. Weissman

TL;DR

This paper critically examines Weissman's recent work on the sum of squares of uniform random variables, comparing it with earlier research on geometric probability, and discusses applications in lattice reduction and random matrix theory.

Contribution

It provides a comparative analysis of Weissman's results with prior work and highlights new applications in lattice reduction and Lyapunov exponents of random matrices.

Findings

Explicit formulas for probabilities are useful in lattice reduction.

Connections between geometric probability and random matrix theory are explored.

The paper clarifies the relationship between recent and earlier results.

Abstract

The recent paper by I. Weissman, "Sum of squares of uniform random variables",[Statist. Probab. Lett. 129 (2017), 147-154] is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersection of a centred ball and cube in $\mathbb R^n$, published in the Problems and Solutions section of SIAM Review in 1997. Some recent applications of explicit formulas for the corresponding probabilities from these references, to problems in lattice reduction, and to the study of Lyapunov exponents of products of random matrices, are noted.