We prove the weak-∗ convergence of a certain sequence of averages of unitary operators associated to the action of the free group on its Gromov boundary. This result, which can be thought as an ergodic theorem à la von Neumann with coefficients, provides a new proof of the irreducibility of the quasi-regular representation of the free group.

This article presents a generalization of the equilibrium analysis for the simple two-player poker game with alternate bidding of Von Neumann and Morgenstern. It approximates optimal play for this game if it is played with a regular deck of 52 cards and it discusses some strategic insights. In addition, the paper studies the relative skill level of this game.

We introduce C∗-pseudo-multiplicative unitaries and (concrete) Hopf C∗-bimodules, which are C∗-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock, Lesieur, and Vallin [5, 6, 4, 10, 19, 20]. Moreover, we associate to every regular C∗-pseudo-multiplicative unitary two Hopf-C∗bimodules and discuss examples related to loca...

In this paper it is shown that two-dimensional cellular automata with Von Neumann neighborhoods are not suitable for cryptographic purposes. This result is obtained after analyzing the most important cryptographic properties of boolean functions defining their local transition rules 2000 Mathematics Subject Classifications: 68Q80, 94A60, 94C10

In von Neumann 29-state cellular automata, the crossing of signals is an important problem, with three solutions reported in the literature. These solutions greatly impact automaton design, especially self-replicators. This paper examines these solutions, with emphasis upon their constructibility. We show that two of these solutions are difficult to construct, and offer an improved design techn...

The celebrated von Neumann minimax theorem is a fundamental theorem in two-person zero-sum games. In this paper, we present a generalization of the von Neumann minimax theorem, called robust von Neumann minimax theorem, in the face of data uncertainty in the payoff matrix via robust optimization approach. We establish that the robust von Neumann minimax theorem is guaranteed for various classes...