✦ LIBER ✦

Probabilistic analysis of column-convex and directed diagonally-convex animals. II: Trajectories and shapes.

✍ Scribed by G. Louchard

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 474 KB
Volume: 15
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199908)15:1<1::aid-rsa1>3.0.co;2-5

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✦ Synopsis

Using some generating functions and limit theorems, we derive a stochastic description of the trajectories and shapes of column-convex and directed diagonally-convex animals for a given large area. The limiting processes are characterized by Brownian motions and the animals' thickness by some discrete distributions, the maximum of which is also analyzed. A simulated realization is constructed for both kind of animals. ᮊ 1999

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Using asymptotic analysis of generating functions, we consider stochastic properties of parameters of some directed animals. For column-convex animals and directed diagonally-convex animals with fixed large area, we obtain asymptotic distribution for the number of columns and the size of a column. W