3.0

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This seminar course will discuss the “probabilistic method,” with applications to random graphs and percolation theory. Topics include linearity of expectation, first and second moment methods, the local lemma, correlation inequalities, martingale concentration results, the evolution of random graphs, Poisson approximation, stochastic ordering, bond and site percolation models, and the substitution method for bounding percolation thresholds. Students will present at least two short talks on relevant topics or applications of their choice. Prerequisites: 553.620 Introduction to Probability and 553.672 Graph Theory, or equivalents. No auditors permitted.