Random geometry (and random topology):

Papers listed here fall into 6 categories:

• studies of random tessellations (marked *)
• models for random sets in space (marked *)
• spatial problems which might be called "random topology" (marked *)
• random packing (marked *)
• the dynamics of shape (marked *)
• miscellaneous (marked *).

For discussion follow the links above or use the downloads given below (authorised by The Applied Probability Trust).

*7. Parker P. & Cowan, R. Some properties of line-segment processes. J. Appl. Prob. 13 96-107 (1976).

*10. Cowan, R. The uses of the ergodic theorems in random geometry. Adv. Appl. Prob. 10 36-46 (1978).

*14. Cowan, R. Properties of ergodic random mosaic processes. Mathematische Nachrichten 97 89-102 (1980).

*15. Cowan, R. Homogeneous line segment processes. Mathematical Proceedings of the Cambridge Philosophical Society 86 481-489 (1979).

*19. Cowan, R. Lectures notes on the theory of point processes. Matematyka Stosowana ziii (1978) 5-27.

*26. Cowan, R. A model for Random Packing of Disks in the Neighbourhood of One Disk. SIAM J. Applied Maths. 44, 4 839-853 (1984).

*27. Cowan, R. A collection of problems in random geometry. Stochastic Geometry, Geometric Statistics, Stereology (eds. Weil and Ambartsumian) Teubner (1984).

*37. Cowan, R. A bivariate exponential distribution arising in random geometry. Annals Institute of Mathematical Statistics 39 103-111 (1987).

*40. Cowan, R. and Morris, V. B. Division Rules for Polygonal Cells. J. Theoretical Biology  131 33-42 (1988).

*42. Cowan, R. Objects arranged randomly in space: an accessible theory. Adv. Appl. Prob. 21 543-569 (1989). Download pdf version

*43. Cowan, R. The division of space and the Poisson distribution. Adv. Appl. Prob. 21 233-234 (1989). Download pdf version

*56. Cowan, R. Constraints on the random packing of disks. J. Appl. Prob. 30, 263-268 (1993). Download pdf file

*58. Cowan, R. and A. K. L. Tsang. The falling-leaf mosaic and its equilibrium properties. Adv. Appl. Prob. 26, 54-62 (1994).

*62. Lee, T. and Cowan, R. A stochastic tessellation of digital space. In Mathematical morphology and its applications to image processing, pp217-224. Eds. J. Serra and P. Soille. Kluwer Publishers (1995). Postscript file can be loaded from Thomas Lee's site.

*65. Cowan, R. and Chen, S. The random division of faces in a planar graph. Adv. Appl. Prob. 28, 377-383 (1996). Download postscript version (without figures).

*67. Cowan, R. Shapes of rectangular prisms after repeated random division. Adv. Appl. Prob. 29, 26-37 (1997). Download post-script file.

*68. Chen, F. K. C. and Cowan, R. Invariant distributions for shapes in sequences of randomly-divided rectangles. Adv. Appl. Prob. 31, 1-14 (1999). Download post-script file.

*70. Cowan, R. and Chen, F. K. C. Four interesting problems concerning Markovian shape sequences. Adv. Appl. Prob. 31, 954-968 (1999). Download post-script file.

*73. Cowan, R., Quine, M. and Zuyev, S. Decomposition of Gamma-distributed domains constructed from Poisson point processes. Adv. Appl. Prob. 35, 56-69 (2003). Download pdf file.

*73(a). Cowan, R. Some Delaunay circumdisks and related lunes. Technical Report in support of #73. Download pdf file.

*74. Cowan, R. A mosaic of triangular cells formed with sequential splitting rules. J. Appl. Prob. 41A, 3-15 (2004). Download pdf file.

*75. Cowan, R. and Chiu, S. N. Extension of Deltheil's study on random points in a convex quadrilateral. Adv. Appl. Prob. 37, 857-58 (2005). Download pdf file.

*75(a). Cowan, R. and Chiu, S. N. A solution of Sylvester-like problems for convex quadrilaterals. Technical Report in support of #75. Download pdf file.

*76. Cowan, R. A more comprehensive Complementary Theorem for the analysis of Poisson point processes. Adv. Appl. Prob. 38, 581-601 (2006). Download pdf file.

*77. Cowan, R. Identities linking volumes of convex hulls. Adv. Appl. Prob. 39, 630-640 (2007). Download pdf file.

*78. Cowan, R.  Recurrence relationships for the mean number of faces and vertices for random convex hulls. Discrete & Computational Geometry, (2008). Download personal-archive pdf version. The original publication is available at www.springerlink.com .

*80. Cowan, R. New classes of random tessellations arising from iterative division of cells. Adv. Appl. Prob. 42, 26-47 (2010). Download pdf file.

*81. Cowan, R. and Miles, R. E. Convex hulls on a hemisphere. Adv. Appl. Prob. 41, 1002-1004 (2009). Download pdf file.

*82. Weiss, V. and Cowan, R. Topological relationships in spatial tessellations. Adv. Appl. Prob. 43, 963-984 (2011). Download pdf file.

*83. Burridge, J., Cowan, R. and Ma, I.  Full and half Gilbert tessellations with rectangular cells. Adv. Appl. Prob. 45, 1-19 (2013). Download pdf file.

*84. Cowan, R.  Line segments in the isotropic planar STIT tessellation. Adv. Appl. Prob. 45, 295-311 (2013). Download pdf file.

*85. Cowan, R. and Thäle, C. The character of planar tessellations which are not side-to-side. Image Analysis and Stereology. 33, 39-54 (2014).

*86. Cowan, R. and Weiss, V. Constraints on the fundamental topological parameters of spatial tessellations. Mathematische Nachrichten. 288, 540-565 (2015). Download pdf file.

*86(a). Cowan, R. and Weiss, V. Graphical presentation of the 7-dimensional parameter space for tessellations of R^3. Technical Report in support of #86. Download pdf file.

*87. Nguyen, N. L., Weiss, V. and Cowan, R. Column tessellations. Image Analysis and Stereology. 34, 87-100 (2015)

*89. Burridge, J. and Cowan, R.  Planar tessellations that have the half-Gilbert structure. Adv. Appl. Prob. 48, 574-584 (2016).

*90. Cowan, R. and Weiss, V. General exchange formulae for random tessellations and other stationary structures. In preparation.

*91 Weiss, V. and Cowan, R. Random tessellations and tilings. (Book in preparation)

 *92. Cowan, R. and Weiss, V. Line segments which are unions of tessellation edges. Image Analysis and Stereology, 37, 83-98 (2018)
 

Link to Richard Cowan's front page.