Mathematical Sciences: Topics in Probability Theory: Statistical Mechanics Type Models and Sums of Independent Random Variables

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Several problems in probability theory are to be studied. The first three concern models which are closely related to statistical physics, while the last one deals with the more traditional topic of sums of independent, identically distributed random variables. Particular problems include finding bounds on the radius of a stochastic growth model, investigating some properties of random resistor networks, and studying the asymptotic shape of first and last passage percolation. This research will investigate some probabilistic models inspired by statistical physics. These include critical phenomena in percolation theory, diffusion limited aggregation , and first-passage percolation. In addition, the investigator will also look at criteria for divergence of sums of independent, identically distributed random variables from which some large summands have been removed.