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Concentration of $k$-th pairwise distance of random points in a unit square

For $1\leq i \leq n$, let $X_i\sim \text{Uniform}(0,1)$, $Y_i \sim \text{Uniform}(0,1)$ be $n$ points chosen uniformly in the unit square. Denote the $k$-th smallest pairwise distances across the $n$ …
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Concentration of $k$-th pairwise distance of random points in a unit square

Just came across this paper on arxiv and remembered I posted this question here last year. This is specifically regarding my Question 2. I thought to post an answer. The authors studied a similar prob …
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