Probability Seminar Department of Statistics and Department of Mathematics Monday, November 4, 2002 3:30 PM in REC 113 Professor Russell Lyons Indiana University and Georgia Tech will speak on Stationary Determinantal Processes (Fermionic Lattice Gases) Abstract Given a measurable function f on the d-dimensional torus with values in the unit interval, there is a 2-state stationary random field on the d-dimensional integer lattice that is defined via minors of the d-dimensional Toeplitz matrix of the function f. The variety of such systems includes certain combinatorial models, certain finitely dependent models, and certain renewal processes in one dimension. Among the interesting properties of these processes, we focus mainly on whether they have a phase transition analogous to that which occurs in statistical mechanics. We describe necessary and sufficient conditions on f for the existence of such a phase transition and give several examples to illustrate the theorem. This is joint work with Jeff Steif.

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