System-size independence of a large deviation function for frequency of events in a one-dimensional forest-fire model with a single ignition site

摘要

It is found that a large deviation function for the frequency of events of a size not equal to the system size in the one-dimensional forest-fire model with a single ignition site at an edge is independent of the system size, by using an exact decomposition of the modified transition matrix of a master equation. An exchange in the largest eigenvalue of the modified transition matrix may not occur in the model.