For d ≥ 3 and correlations bounded by g satisfying a specific integral condition, the superprocess converges to a non-trivial stationary measure with mean Lebesgue measure, answering a 2007 conjecture; strong correlations cause local extinction.
From B rownian motion to S chr\" o dinger's equation , volume 312 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
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Persistence and local extinction for superprocesses in random environments
For d ≥ 3 and correlations bounded by g satisfying a specific integral condition, the superprocess converges to a non-trivial stationary measure with mean Lebesgue measure, answering a 2007 conjecture; strong correlations cause local extinction.