Rényi's Parking Constants

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Given the Closed Interval with , let 1-D ``cars'' of unit length be parked randomly on the interval. The Mean number of cars which can fit (without overlapping!) satisfies

(1)

			(2)

(3)

(4)

(5)

Let be the variance of the number of cars, then Dvoretzky and Robbins (1964) and Mannion (1964) showed that

			(6)

where

			(7)
			(8)

(9)

(10)

Palasti (1960) conjectured that in 2-D,

(11)

References

Blaisdell, B. E. and Solomon, H. ``On Random Sequential Packing in the Plane and a Conjecture of Palasti.'' J. Appl. Prob. 7, 667-698, 1970.

Dvoretzky, A. and Robbins, H. ``On the Parking Problem.'' Publ. Math. Inst. Hung. Acad. Sci. 9, 209-224, 1964.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/renyi/renyi.html

Mannion, D. ``Random Space-Filling in One Dimension.'' Publ. Math. Inst. Hung. Acad. Sci. 9, 143-154, 1964.

Palasti, I. ``On Some Random Space Filling Problems.'' Publ. Math. Inst. Hung. Acad. Sci. 5, 353-359, 1960.

Rényi, A. ``On a One-Dimensional Problem Concerning Random Space-Filling.'' Publ. Math. Inst. Hung. Acad. Sci. 3, 109-127, 1958.

Solomon, H. and Weiner, H. J. ``A Review of the Packing Problem.'' Comm. Statist. Th. Meth. 15, 2571-2607, 1986.

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