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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
This text focuses on percolation theory - the study of an idealized random medium in two or more dimensions. Percolation is pivotal for studying more complex physical systems …
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 …
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 …