  The one-dimensional forest-fire model including lightnings is studied
numerically and analytically. For the tree correlation function, a new
correlation length with critical exponent \nu ~ 5/6 is found by simulations. A
Hamiltonian formulation is introduced which enables one to study the stationary
state close to the critical point using quantum-mechanical perturbation theory.
With this formulation also the structure of the low-lying relaxation spectrum
and the critical behaviour of the smallest complex gap are investigated
numerically. Finally, it is shown that critical correlation functions can be
obtained from a simplified model involving only the total number of trees
although such simplified models are unable to reproduce the correct
off-critical behaviour.
