We show that a sequence of voter models, suitably rescaled in space and time,converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
(Note that the results hold if occupied sites are sufficiently sparse.)
Description
MR: Publications results for "MR Number=(1756003)"
%0 Journal Article
%1 MR1756003
%A Cox, J. Theodore
%A Durrett, Richard
%A Perkins, Edwin A.
%D 2000
%J The Annals of Probability
%K branching_Brownian_motion particle_systems voter_model
%N 1
%P 185--234
%R 10.1214/aop/1019160117
%T Rescaled voter models converge to super-Brownian motion
%U http://dx.doi.org/10.1214/aop/1019160117
%V 28
%X We show that a sequence of voter models, suitably rescaled in space and time,converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
(Note that the results hold if occupied sites are sufficiently sparse.)
@article{MR1756003,
abstract = {We show that a sequence of voter models, suitably rescaled in space and time,converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
(Note that the results hold if occupied sites are sufficiently sparse.)},
added-at = {2012-08-27T19:36:01.000+0200},
author = {Cox, J. Theodore and Durrett, Richard and Perkins, Edwin A.},
biburl = {https://www.bibsonomy.org/bibtex/272f846ae50c3ed4756c2767aae526b35/peter.ralph},
coden = {APBYAE},
description = {MR: Publications results for "MR Number=(1756003)"},
doi = {10.1214/aop/1019160117},
interhash = {216d47be07277a0cab3de0cc2f53cf24},
intrahash = {72f846ae50c3ed4756c2767aae526b35},
issn = {0091-1798},
journal = {The Annals of Probability},
keywords = {branching_Brownian_motion particle_systems voter_model},
mrclass = {60K35 (60F05 60G57 60J80)},
mrnumber = {1756003 (2001d:60105)},
mrreviewer = {Luis G. Gorostiza},
number = 1,
pages = {185--234},
sjournal = {Ann. Probab.},
timestamp = {2012-08-27T19:36:01.000+0200},
title = {Rescaled voter models converge to super-{B}rownian motion},
url = {http://dx.doi.org/10.1214/aop/1019160117},
volume = 28,
year = 2000
}