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Answer by Marcus M for Randomly removing length 1 intervals in an interval (a...
This is exactly the so-called "Renyi parking process." Renyi proved$$\varphi(x) = cx + c - 1 + o(1)$$where $$c = \int_0^\infty \exp\left( -2 \int_0^x \frac{1 - e^{-y}}{y}\,dy \right)\,dx \approx...
View ArticleRandomly removing length 1 intervals in an interval (a fragmentation process)
Short version: Start with a closed interval of length $t>0$ and repeatedly remove a random and uniformly distributed subinterval of length $1$ so long as this is possible. For $t$ large, what is the...
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