POISSON PROCESS INVARIANT MEASURE PERCOLATION SPATIAL POINT PROCESSES LOSS NETWORK SILO STRESS SIMULATION BIRTH AND DEATH PROCESSES INTERACTING PARTICLE SYSTEMS INFINITE RANGE INTERACTION KALIKOW-TYPE DECOMPOSITION CHAINS OF INFINITE ORDER CLAN OF ANCESTORS GIBBS MEASURE SPATIAL GIBBS RANDOM GRAPHS COUPLING VARIABLE LENGTH MARKOV CHAIN ISING MODEL