ON THE WEAK LIMIT LAW OF THE MAXIMAL UNIFORM $k$-SPACING

Abstract. This paper gives a simple proof of a limit theorem for the length of the largest interval straddling a fixed number of i.i.d. points uniformly distributed on a unit interval. The key step in our argument is a classical theorem of [Watson, Ann. Math. Stat., 1954] on the maxima of $m$-dependent stationary stochastic sequences.

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