%0 Journal Article %1 gilbert-crystallization %A Gilbert, E. N. %D 1962 %J Ann. Math. Statist. %K Johnson-Mehl crystalization %P 958--972 %T Random subdivisions of space into crystals %U http://projecteuclid.org/euclid.aoms/1177704464 %V 33 %X There are two main models for random subdivisions of the $n$-dimensional space into disjoint regions, namely, the cell model of J. L. Meijering Philips Res. Rep. 8 (1953), 270--290 and a more complicated model indicated by W. A. Johnson and R. F. Mehl Trans. Amer. Inst. Mining Metal. Engrs. 135 (1939), 416--458. The regions can be considered as crystals, cells, bubbles or detection regions of a code. For both models several mean values, like the mean surface area, mean number of faces and the mean total edge length, have been calculated. The author continues the study of both models and is in particular interested in finding the variance of the volume of a crystal and the variances of plane or line sections through crystals. He also obtains bounds on the distribution functions for crystal volumes.

@article{gilbert-crystallization, abstract = {There are two main models for random subdivisions of the $n$-dimensional space into disjoint regions, namely, the cell model of J. L. Meijering [Philips Res. Rep. 8 (1953), 270--290] and a more complicated model indicated by W. A. Johnson and R. F. Mehl [Trans. Amer. Inst. Mining Metal. Engrs. 135 (1939), 416--458]. The regions can be considered as crystals, cells, bubbles or detection regions of a code. For both models several mean values, like the mean surface area, mean number of faces and the mean total edge length, have been calculated. The author continues the study of both models and is in particular interested in finding the variance of the volume of a crystal and the variances of plane or line sections through crystals. He also obtains bounds on the distribution functions for crystal volumes. }, added-at = {2009-11-25T17:49:11.000+0100}, author = {Gilbert, E. N.}, biburl = {https://www.bibsonomy.org/bibtex/2706af0a4b2aeeaff8ace842f03103a49/peter.ralph}, description = {MR: Publications results for "MR Number=(144253)"}, fjournal = {Annals of Mathematical Statistics}, interhash = {608b2c6fa7fa6903e35e6342ebfce619}, intrahash = {706af0a4b2aeeaff8ace842f03103a49}, issn = {0003-4851}, journal = {Ann. Math. Statist.}, keywords = {Johnson-Mehl crystalization}, mrclass = {50.90}, mrnumber = {MR0144253 (26 \#1800)}, mrreviewer = {H. Bauer}, pages = {958--972}, timestamp = {2009-11-25T17:49:11.000+0100}, title = {Random subdivisions of space into crystals}, url = {http://projecteuclid.org/euclid.aoms/1177704464}, volume = 33, year = 1962 }