The Expected Perimeter in Eden and Related Growth Processes

Details The Expected Perimeter in Eden and Related Growth Processes The Expected Perimeter in Eden and Related Growth Processes

2010-11-08

arxiv.org/abs/1011.1881v1

Mathematics

Combinatorics

11 pages

Scientific paper

Following Richardson and using results of Kesten on First-passage
percolation, we obtain an upper bound on the expected perimeter in an Eden
Growth Process. Using results of the author from a problem in Statistical
Mechanics, we show that the average perimeter of the lattice animals resulting
from a very natural family of "growth histories" does not obey a similar bound.

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