The Expected Perimeter in Eden and Related Growth Processes
arXiv:1011.1881 · doi:10.1007/s00548-010-0128-y
Abstract
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.
11 pages