ALGEBRAIC L(2) DECAY OF ATTRACTIVE CRITICAL PROCESSES ON THE LATTICE

We consider a special class of attractive critical processes based on the transition function of a transient random walk on Z(d). These proc esses have infinitely many invariant distributions and no spectral gap . The exponential L2 decay is replaced by an algebraic L2 decay. The p aper shows the dependence of this algebraic rate in terms of the dimen sion of the lattice and the locality of the functions under considerat ion. The theory is illustrated by several examples dealing with locall y interacting diffusion processes and independent random walks.