1301.2369 (Yukio Hayashi et al.)

Combinatorial and approximative analyses in spatially random division
process    [PDF]

Yukio Hayashi, Takayuki Komaki, Yusuke Ide, Takuya Machida, Norio Konno

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.

View original: http://arxiv.org/abs/1301.2369