Stochastic dynamics of Ising models at zero temperature

This thesis studies certain spin flip dynamics, known as zero-temperature stochastic Ising models, related cellular automata, and the percolation models that arise from the action of those dynamics on independent, spin-percolation configurations.; Zero-temperature stochastic Ising models can be obtained as suitable zero-temperature limits of Glauber dynamics, and can be used to study the behavior of different kinds of magnetic systems following a deep “quench” from infinite temperature to zero temperature. This is a central topic in nonequilibrium statistical mechanics, with a vast literature.; The main results presented here, obtained in different collaborations with various people and contained in papers cited in the references, concern particular aspects of the long-time behavior of the dynamics, such as the speed of convergence to a final state or transience and recurrence of local configurations when no final state is reached, and the determination of the continuum scaling limit of the percolation processes considered. This last result provides an explicit example of a form of universality for two-dimensional percolation.