= Cyclic interval overlap bound
{title2=$\mathbb P(S\cap T\ne\varnothing)\leq2k/d$}
For independent uniformly placed cyclic intervals of length $k<d$, an overlap is possible at at most $2k-1$ starting-point offsets, or at all $d$ offsets if that number exceeds $d$. Thus the overlap <probability> is at most $\min\{1,(2k-1)/d\}$. If $R=|S\cap T|$, then $0\leq R\leq k$ and $\mathbb E(e^{aR/k}-1)\leq(2k/d)(e^a-1)$ for $a\geq0$. The overlap law is not the <hypergeometric distribution> for unrestricted random subsets.
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