%0 Journal Article %1 bramson2001superbrownian %A Bramson, Maury %A Cox, J. Theodore %A Le Gall, Jean-Francois %D 2001 %J Ann. Probab. %K branching_Brownian_motion particle_system random_sets voter_model %N 3 %P 1001--1032 %R 10.1214/aop/1015345592 %T Super-Brownian limits of voter model clusters %U http://dx.doi.org/10.1214/aop/1015345592 %V 29 %X The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (1) sharing the same opinion as the site 0, and (2) having the opinion that was originally at 0. Results on the sizes of these sets were given by Sawyer (1979) and Bramson and Griffeath (1980). Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from Cox, Durrett and Perkins (2000) serves as an important tool for these results.

@article{bramson2001superbrownian, abstract = {The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (1) sharing the same opinion as the site 0, and (2) having the opinion that was originally at 0. Results on the sizes of these sets were given by Sawyer (1979) and Bramson and Griffeath (1980). Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from Cox, Durrett and Perkins (2000) serves as an important tool for these results. }, added-at = {2012-08-27T19:51:16.000+0200}, author = {Bramson, Maury and Cox, J. Theodore and Le Gall, Jean-Fran{\c{c}}ois}, biburl = {https://www.bibsonomy.org/bibtex/2027fb68ed1b2f0aea178edeffbc7ac4d/peter.ralph}, coden = {APBYAE}, description = {MR: Selected Matches for: Title=(voter model)}, doi = {10.1214/aop/1015345592}, fjournal = {The Annals of Probability}, interhash = {1c53194d539ab1a3fa552db7b955c10e}, intrahash = {027fb68ed1b2f0aea178edeffbc7ac4d}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {branching_Brownian_motion particle_system random_sets voter_model}, mrclass = {60K35 (60F05 60G57 60J80)}, mrnumber = {1872733 (2003c:60160)}, mrreviewer = {Min Kang}, number = 3, pages = {1001--1032}, timestamp = {2012-08-27T19:51:16.000+0200}, title = {Super-{B}rownian limits of voter model clusters}, url = {http://dx.doi.org/10.1214/aop/1015345592}, volume = 29, year = 2001 }