Algebraic \(L^ 2\) decay of attractive critical processes on the lattice
The algebraic decay and convergence in \(L^ 1\) \((L^ p)\) is investigated for a class of linear attractive processes which are described using a transient random walk. The dependence of the decay of \(\| P_ t f-\langle f\rangle\|_ p\) on the dimension as well as on the locality of the function \(f\) is studied. Both the estimates from below and from above are obtained. These results are applied to interacting Ornstein-Uhlenbeck processes, a branching random walk, and the ``stepping stone'' models. The last section is devoted to processes described by the use of a product measure (independent random walk) instead of the transient random walk.
interacting Ornstein-Uhlenbeck processes
scientific article; zbMATH DE number 567185