We initiate the study of general neighborhood growth dynamics on two-dimensional Hamming graphs. The decision to add a point is made by counting the currently occupied points on the horizontal and the vertical line through it, and checking whether the pair of counts lies outside a fixed Young diagram. We focus on two related extremal quantities. The first is the size of the smallest set that eventually occupies the entire plane. The second is the minimum of an energy-entropy functional that comes from the scaling of the probability of eventual full occupation versus the density of the initial product measure within a rectangle. We demonstrate the existence of this scaling and study these quantities for large Young diagrams.
@article{10_37236_6400,
author = {Janko Gravner and David Sivakoff and Erik Slivken},
title = {Neighborhood growth dynamics on the {Hamming} plane},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/6400},
zbl = {1373.05092},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6400/}
}
TY - JOUR
AU - Janko Gravner
AU - David Sivakoff
AU - Erik Slivken
TI - Neighborhood growth dynamics on the Hamming plane
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6400/
DO - 10.37236/6400
ID - 10_37236_6400
ER -
%0 Journal Article
%A Janko Gravner
%A David Sivakoff
%A Erik Slivken
%T Neighborhood growth dynamics on the Hamming plane
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6400/
%R 10.37236/6400
%F 10_37236_6400
Janko Gravner; David Sivakoff; Erik Slivken. Neighborhood growth dynamics on the Hamming plane. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6400
