2
votes
1answer
42 views

Square Line Picking

The probability density function of the distance between two points chosen randomly on the unit square is given by: $ P(\ell) = \begin{cases} 2\ell\left(\ell^2 - 4\ell + \pi\right) & 0 \leq \ell ...
3
votes
0answers
135 views

Integral Geometry Reference Request

I am looking for a good introductory reference (book, lecture notes, survey article) on integral geometry. I am especially interested in the Crofton formula in $\mathbb{R}^n$ and its extensions to ...
1
vote
3answers
215 views

Cover a line segment randomly with smaller line segments

Covering a circle randomly with arcs has been well studied in the past (Geometric Probability - Solomon). But the problem when the circle is changed to a line segment doesn't seem to have been ...