Space-time percolation
| dc.creator | Grimmett, Geoffrey | |
| dc.date | 2007-05-03 | |
| dc.date.accessioned | 2026-07-07T07:59:19Z | |
| dc.date.available | 2026-07-07T07:59:19Z | |
| dc.description | The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly complete analysis of the contact model at and near its critical point. The corresponding process when the time-axis is unoriented is an undirected percolation model to which now standard techniques may be applied. One may construct in similar vein a random-cluster model on $\ZZ \times \RR$, with associated continuum Ising and Potts models. These models are of independent interest, in addition to providing a path-integral representation of the quantum Ising model with transverse field. This representation may be used to obtain a bound on the entanglement of a finite set of spins in the quantum Ising model on $\ZZ$, where this entanglement is measured via the entropy of the reduced density matrix. The mean-field version of the quantum Ising model gives rise to a random-cluster model on $K_n \times \RR$, thereby extending the Erdos-Renyi random graph on the complete graph $K_n$. | |
| dc.identifier | https://arxiv.org/abs/0705.0506 | |
| dc.identifier | http://arxiv.org/abs/0705.0506 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128326 | |
| dc.subject | Probability | |
| dc.subject | 60K35 | |
| dc.title | Space-time percolation | |
| dc.type | text |