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George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.

Algebra. --- Ordered algebraic structures. --- Convex geometry . --- Discrete geometry. --- Polytopes. --- Order, Lattices, Ordered Algebraic Structures. --- Convex and Discrete Geometry.

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Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Polytopes. --- Probabilities. --- Combinatorics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Stochastic analysis. --- Poisson processes. --- Processes, Poisson --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Point processes --- Distribution (Probability theory. --- Math --- Science --- Combinatorics --- Algebra --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Engineering --- Engineering analysis --- Hyperspace --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk