| 释义 |
Rényi's Parking ConstantsN.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) |
 is
Furthermore,
 | (3) |
 (Rényi 1958), which was strengthened by Dvoretzky and Robbins (1964) to
 | (4) |
 | (5) |
Let  be the variance of the number of cars, then Dvoretzky and Robbins (1964) and Mannion (1964) showed that
where
and the numerical value is due to Blaisdell and Solomon (1970). Dvoretzky and Robbins (1964) also proved that
 | (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. |
