Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains

Abstract

We develop a technique for establishing statistical tests with precise confidence levels for upper bounds on the critical probability in oriented percolation. We use it to givepc< 0.647 with a 99.999967% confidence. As Monte Carlo simulations suggest thatpc≈ 0.6445, this bound is fairly tight.