MARTINGALES ON TREES AND PERCOLATION by Davar Khoshnevisan Department of Mathematics, University of Utah INSCC 110, 3:30pm Tesday, February 16, 1999 Abstract I will introduce and describe some key properties for a large class of stochastic processes (called martingales) which are indexed by trees. These are quite related to Doob's martingale processes indexed by the real line. As an application of the general theory, I will provide an abstract proof of some well--known results of Russell Lyons on percolation on trees. Request for preprints and reprints to Davar Khoshnevisan This information can be found at http://www.math.utah.edu/research/