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Lectures on Probability Theory and Statistics
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Probability on Discrete Structures
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. …
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 …
The 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 …
Percolation Theory at Saint-Flour
Grimmett, Geoffrey: Percolation and disordered systems.- Kesten, Harry: Aspects of first passage percolation.?
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 …