QUANTUM OPERATORS IN CLASSICAL PROBABILITY-THEORY .1. QUANTUM SPIN TECHNIQUES AND THE EXCLUSION MODEL OF DIFFUSION

The exclusion process is an interacting particle system in which parti cles perform random walks on a lattice except that they may not move t o a position already occupied. In this paper we show how techniques de rived from quantum mechanics may be used to achieve asymptotic results for an exclusion process on a complete graph. In particular, an abrup t approach to stationarity is demonstrated. The similarity between the transition matrix for the exclusion process and the Hamiltonian for t he Heisenberg ferromagnet is not well understood. However, it allows n ot only quantum operator techniques to be carried over to a problem in stochastic processes, but also concepts such as the ''mean field''.