Maximal Minimal Spacing for Random Points (opens in new tab)

From $N+1$ random points on a line we wish to select $M+1$ points so as to maximize the minimal spacing between them. We consider an initial configuration with independent and identically distributed spacings. The problem is equivalent to optimally grouping consecutive gaps into $M$ blocks and maximizing the smallest block sum. For general gap distributions, and for all $M\leq N$, we derive exact distributional identities for the optimal spaci...