B. P. Weiss

On the class of systems which are disjoint from every ergodic system

In this note, we give a fairly direct proof of a recent theorem of Górska, Lemańczyk and de la Rue which characterises the class of measure-preserving transformations that are disjoint from every ergodic measure-preserving transformation. Our proof works just as well for any coun...

Monotonicity, topology, and convexity of recurrence in random walks

We consider nonhomogeneous random walks on the two-dimensional positive quadrant N2. In the 1960’s the following question was asked for N2: is it true if such a random walk X is recurrent and Y is another random walk that at every point is more likely to go down and more likely t...