Fixation for Two-Dimensional $\mathcal U$-ISING and $\mathcal U$-VOTER Dynamics

@article{Blanquicett2020FixationFT,
  title={Fixation for Two-Dimensional \$\mathcal U\$-ISING and \$\mathcal U\$-VOTER Dynamics},
  author={Daniel Blanquicett},
  journal={arXiv: Probability},
  year={2020}
}
Given a finite family $\mathcal U$ of finite subsets of $\mathbb Z^d\setminus \{0\}$, the $\mathcal U$-$voter\ dynamics$ in the space of configurations $\{+,-\}^{\mathbb Z^d}$ is defined as follows: every $v\in\mathbb Z^d$ has an independent exponential random clock, and when the clock at $v$ rings, the vertex $v$ chooses $X\in\mathcal U$ uniformly at random. If the set $v+X$ is entirely in state $+$ (resp. $-$), then the state of $v$ updates to $+$ (resp. $-$), otherwise nothing happens. The… Expand

Figures from this paper

References

SHOWING 1-10 OF 19 REFERENCES
Monotone Cellular Automata in a Random Environment
Zero-temperature Glauber dynamics on Z^d
Fixation for coarsening dynamics in 2D slabs
Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature
Bootstrap percolation, and other automata
  • R. Morris
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • 2017
Lectures on Glauber dynamics for discrete spin models
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes
...
1
2
...