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Stochastic Processes on a Lattice and Gibbs Measures (Paperback, Softcover reprint of the original 1st ed. 1991)
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Stochastic Processes on a Lattice and Gibbs Measures (Paperback, Softcover reprint of the original 1st ed. 1991)
Series: Mathematical Physics Studies, 11
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In many domains one encounters "systems" of interacting elements,
elements that interact more forcefully the closer they may be. The
historical example upon which the theory offered in this book is
based is that of magnetization as it is described by the Ising
model. At the vertices of a regular lattice of sites, atoms "choos
e" an orientation under the influence of the orientations of the
neighboring atoms. But other examples are known, in physics (the
theories of gasses, fluids, .. J, in biology (cells are
increasingly likely to become malignant when their neighboring
cells are malignant), or in medecine (the spread of contagious
deseases, geogenetics, .. .), even in the social sciences (spread
of behavioral traits within a population). Beyond the spacial
aspect that is related to the idea of "neighboring" sites, the
models for all these phenomena exhibit three common features: - The
unavoidable ignorance about the totality of the phenomenon that is
being studied and the presence of a great number of often
unsuspected factors that are always unquantified lead inevitably to
stochastic models. The concept of accident is very often inherent
to the very nature of the phenomena considered, so, to justify this
procedure, one has recourse to the physicist's principle of
indeterminacy, or, for example, to the factor of chance in the
Mendelian genetics of phenotypes.
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