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Probabilistic analysis of column‐convex and directed diagonally‐convex animals. II: Trajectories and shapes.
Author(s) -
Louchard G.
Publication year - 1999
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199908)15:1<1::aid-rsa1>3.0.co;2-5
Subject(s) - mathematics , regular polygon , realization (probability) , probabilistic logic , diagonal , convex analysis , limit (mathematics) , limiting , convex combination , struct , combinatorics , mathematical analysis , geometry , convex optimization , computer science , statistics , engineering , mechanical engineering , programming language
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. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15: 1–23, 1999