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Lectures on Probability Theory and Statistics
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Percolation
Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty …
Random-Cluster Model
Therandom-clustermodelwasinventedbyCees[Kees]FortuinandPietKasteleyn around 1969 as a uni?cation of percolation, Ising, and Potts models, and as an extrapolation of electrical …
Mathematics of Multiscale Materials
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shape-memory metals, magnetic materials, and …