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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 $\mathbb{Z}^d$. These processes have infinitely many invariant distributions and no spectral gap. The exponential $L^2$ decay is replaced by an algebraic $L^2$ decay. The paper shows the dependence of this …