Some properties of line segment processes
- 1 March 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (1) , 96-107
- https://doi.org/10.2307/3212669
Abstract
This paper formulates the random process of line-segments in the Euclidean plane. Under conditions more general than Poisson, expressions are obtained, for BorelA⊂R2, for the first moments ofM(A), the number of segment mid-points inA;N(A), the number of segments which intersect with convexA;S(A), the total length withinAof segments crossingA; andC(A) the number of segment-segment crossings withinA. In the case of Poisson mid-points, the distribution of therth nearest line-segment to a given point is found.Keywords
This publication has 6 references indexed in Scilit:
- On the transport of compact particles through solutions of chain-polymersProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1973
- Sampling procedures for the lengths of random straight linesBiometrika, 1972
- Spatial Variability and the Theory of Sampling in Random Fibrous NetworksJournal of the Royal Statistical Society Series B: Statistical Methodology, 1971
- Random-drift sampling—A study by computer simulationNuclear Instruments and Methods, 1968
- RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANEProceedings of the National Academy of Sciences, 1964
- The spaces in a uniform random suspension of fibresTransactions of the Faraday Society, 1958