Pointwise ergodic theorem for locally countable quasi-pmp graphs

Menger's theorem for countable graphs

For a finite graph G= (I’, E) Menger’s Theorem [6] states the following: if A, B c V then the minimal size of an A -B separating set of vertices (i.e., a set whose removal disconnects A from B), equals the maximal size of a set of disjoint A -B paths. This version of the theorem remains true, and quite easy to prove, also in the infinite case. To see this, take 9 to be a maximal (with respect t...

A Quasi-ergodic Theorem for Evanescent Processes

We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a convergence result for conditioned processes as the conditioning event becomes rarer.

A Pointwise Ergodic Theorem for Imprecise Markov Chains

We prove a game-theoretic version of the strong law of large numbers for submartingale differences, and use this to derive a pointwise ergodic theorem for discrete-time Markov chains with finite state sets, when the transition probabilities are imprecise, in the sense that they are only known to belong to some convex closed set of probability measures.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Countable locally 2-arc-transitive bipartite graphs

We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We give several new families of previously unknown countably infinite locally-2-arc-transitive graphs, each family containing continuum many members. These exampl...