Competition processes on a lattice

Extract

Some years ago Hammersley and Clifford considered the problem of assigning probabilities to colourings of a graph according to certain local conditions. Subsequent expositions such as those of Grimmett, Besag and Preston, whilst providing more elegant derivations, have shown that the assignment of probabilities coincides with the limiting distribution of spatial-temporal processes arising from theoretical physics. There has been relatively little work on spatial-temporal processes outside this class. In this paper the approximate behaviour of an alternative class of processes is investigated. Topics will include statistical estimation of parameters and existence of unique equilibria.