Probability and Stochastic Processes Frank Gao, Paul Joyce, and Steve Krone. Our work in probability focuses on stochastic processes and their applications. Topics of current interest include interacting particle systems and percolation theory, population genetics, limit theorems, majorizing measures and applications to Banach spaces, etc. Interacting particle systems are useful for modeling random phenomena with spatial structure. These stochastic processes live on a d-dimensional integer lattice or some other (infinite) graph. Each site can be in one of several states, and a site changes its state at rates that depend on the states of nearby sites (local interactions). The number and interpretation of the "states" depends on the application. We might be interested in whether or not a site is occupied by a particle, or whether a site is occupied by different species. These species might be competing with each other for space, for example. The types of questions that are typically addressed are things like long-term survival or extinction of a certain type of "particle," coexistence of several types, clustering of occupied sites, etc. Interacting particle systems were originally studied in connection with models in statistical physics, but in recent years there has been a strong emphasis on applications to population biology and spatial models in ecology. It is very natural in this setting, since one typically has spatially distributed systems with local interactions. Our work in population genetics has centered on things like coalescent theory, liklihood methods, and other statistical procedures. In coalescent theory, one is interested in the ancestry of a sample from a population (at a particular genetic locus). This backwards-looking approach is at the heart of much of modern population genetics. Correct interpretation of genetic data often requires sophisticated mathematical models and new data analysis techniques. Another major part of our current research effort has focused on sampling distributions and the inferences that can be drawn from them. The sample is often a collection of DNA sequences. What is the best way to summarize the observed amount of DNA polymorphism in a data set? How does one use these summary statistics to make valid inferences about aspects of the population, such as effective population size, substitution rates, selection coefficients and time to a common ancestor? We try to answer these questions and account for errors in our conclusions by using probabilistic models and statistical methods. Our work also covers majorizing measures and their applications in local theory of Banach spaces. Majorizing measures were developed by Fernique and Talagrand as the tool to characterize the sample boundedness and sample continuity of general Gaussian processes. Later on it turned out to be a very powerful tool in other settings as well. To futher develop and utilize this tool, one needs to study the majorizing measures in non-Hilbert spaces. Currently, we are working on the majorizing measures in type-2 Banach spaces. The difficulty here is that in such settings, we lack the connection between the majorizing measures and the Gaussian processes.