Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$
Cox, J. T.
Ann. Probab., Tome 17 (1989) no. 4, p. 1333-1366 / Harvested from Project Euclid
Let $\eta_t$ be the basic voter model on $\mathbb{Z}^d$ and let $\eta^{(N)}_t$ be the voter model on $\Lambda(N)$, the torus of side $N$ in $\mathbb{Z}^d$. Unlike $\eta_t, \eta^{(N)}_t$ (for fixed $N$) gets trapped with probability 1 as $t \rightarrow\infty$ at all 0's or all 1's. We examine the asymptotic growth of these trapping or consensus times $\tau^{(N)}$ as $N \rightarrow\infty$. To do this we obtain limit theorems for coalescing random walk systems on the torus $\Lambda(N)$, including a new hitting time limit theorem for (noncoalescing) random walk on the torus.
Publié le : 1989-10-14
Classification:  Infinite particle systems,  finite particle systems,  random walks,  voter model,  60K35
@article{1176991158,
     author = {Cox, J. T.},
     title = {Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1333-1366},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991158}
}
Cox, J. T. Coalescing Random Walks and Voter Model Consensus Times on the Torus in $\mathbb{Z}^d$. Ann. Probab., Tome 17 (1989) no. 4, pp.  1333-1366. http://gdmltest.u-ga.fr/item/1176991158/