Coupling surfaces and weak Bernoulli in one and higher dimensions (Q1378455)

Since the natural generalization of the definition of weak Bernoulli in dimension 1 to all dimensions is too strong in higher dimensions, the authors propose a different one. It is based on the notion of a coupling surface and, as it is shown, is equivalent to the usual one in dimension 1. The authors study the relation to quite weak Bernoulli and quite weak Bernoulli with exponential rate, introduced by them in [Stochastic Processes Appl. 58, No. 1, 35-55 (1995; Zbl 0835.60088)]. They also show, that the Ising model with large interaction is weak Bernoulli with an explicit construction of the coupling surface.