In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe–Biggins LLN for super-Brownian ...

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the origin. We prove a strong law of large numbers for the number of particles present at time t in an interval growing linearly with t.

This paper provides micro-foundations for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under independence assumptions at each randomization step, we show that there is an almost-sure constant cross-section...

k=n Ak. If E occurs, then infinitely many of Ak:s occur. Sometimes we write this as E = {An i.o.} where i.o. is to be read as ”infinitely often”, i.e., infinitely many times. E is sometimes denoted with lim supAk. We need a couple of auxiliary results (the lemmas below) of probability calculus (found, e.g., on page 3 of [1]) that are basic in the sense that they are derived directly from the Ko...