Randomized coverings of a convex body with its homothetic copies, and illumination
Galyna Livshyts, Konstantin Tikhomirov

TL;DR
This paper introduces a probabilistic model for illuminating convex bodies using independent light sources, improving bounds on the illumination number and parameter, advancing understanding in geometric covering problems.
Contribution
It develops a probabilistic approach to convex body illumination, refining existing bounds and extending previous estimates in the field.
Findings
Recovered C.A. Rogers' upper bounds for the illumination number.
Improved estimates for a generalized illumination parameter.
Enhanced probabilistic methods for convex body covering.
Abstract
We present a probabilistic model of illuminating a convex body by independently distributed light sources. In addition to recovering C.A. Rogers' upper bounds for the illumination number, we improve previous estimates of J. Januszewski and M. Nasz\'odi for a generalized version of the illumination parameter.
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