Ebook: Spread-out oriented percolation and related models above the upper critical dimension: induction and superprocesses

Abstract. In these notes we give an extensive survey of the recent progress
for critical spread-out oriented percolation above the upper critical dimension.
We describe the main tools, which are the lace expansion and the
inductive method. The lace expansion gives a recursion relation for the
two-point functions involved, and the inductive method gives an inductive
analysis of the arising recursion relation. These results apply also to
self-avoiding walk. We further describe the scaling results for the oriented
percolation higher-point functions, and compare these to their branching
random walk analogues. Finally, we discuss the relations between scaling
limits of critical branching models to super-processes, which are random
measures evolving diffusively in time.