**Title:** Some aspects of determinantal probability measures, I

**Speaker:** Russell Lyons

**Speaker Info:** Indiana University

**Brief Description:**

**Special Note**:

**Abstract:**

(1) For each subset A of the circle with measure m, there is a sequence of integers of Beurling-Malliavin density m such that set of the corresponding complex exponentials is complete for L^2(A).(2) Given an infinite graph, simple random walk on each tree in the wired uniform spanning forest is a.s. recurrent.

(3) In our first talk, we give a theorem that has both these as corollaries. In our second talk, we describe a conjectural analogue for continuous point processes and its applications to zeroes of analytic functions. We also describe the ideas behind the results, which depend on determinantal probability measures.

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