The Page-Rényi parking process (Q888609)

Summary: In the Page parking (or packing) model on a discrete interval (also known as the \textit{discrete Rényi packing} problem or the \textit{unfriendly seating problem}), cars of length two successively park uniformly at random on pairs of adjacent places, until only isolated places remain. We use a probabilistic construction of the Page parking to give a short proof of the (known) fact that the proportion of the interval occupied by cars goes to \(1-e^{-2}\), when the length of the interval goes to infinity. We also obtain some new consequences on both finite and infinite parkings.