Empires and Percolation: Stochastic Merging of Adjacent Regions TeX Export

@article{citeulike:6083732, abstract = {We introduce a stochastic model in which adjacent planar regions \$A, B\$ merge stochastically at some rate \$\lambda(A,B)\$, and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on \$\lambda\$ for this {\em hegemony} property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case \$\lambda(A,B) \equiv 1\$. For this case, a non-rigorous analytic argument and simulations suggest hegemony.}, archivePrefix = {arXiv}, author = {Aldous, D. J. and Ong, J. R. and Zhou, W.}, citeulike-article-id = {6083732}, citeulike-linkout-0 = {http://arxiv.org/abs/0911.0601}, citeulike-linkout-1 = {http://arxiv.org/pdf/0911.0601}, day = {3}, eprint = {0911.0601}, keywords = {coagulation, percolation}, month = {Nov}, posted-at = {2009-11-08 08:09:16}, priority = {2}, title = {Empires and Percolation: Stochastic Merging of Adjacent Regions}, url = {http://arxiv.org/abs/0911.0601}, year = {2009} }

TY - JOUR ID - citeulike:6083732 L3 - citeulike-article-id:6083732 N2 - We introduce a stochastic model in which adjacent planar regions $A, B$ merge stochastically at some rate $\lambda(A,B)$, and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on $\lambda$ for this {\em hegemony} property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case $\lambda(A,B) \equiv 1$. For this case, a non-rigorous analytic argument and simulations suggest hegemony. TI - Empires and Percolation: Stochastic Merging of Adjacent Regions KW - coagulation KW - percolation AU - Aldous, DJ AU - Ong, JR AU - Zhou, W PY - 2009/Nov/03/ UR - http://arxiv.org/abs/0911.0601 ER -