The self-avoiding walk is a mathematical model that has
important applications in statistical mechanics and polymer
science. In spite of its simple definition a path on a lattice that
does not visit the same site more than once it is difficult to
analyze mathematically. "TheSelf-Avoiding Walk"provides the
firstunified account of the known rigorous results for the
self-avoiding walk, with particular emphasis on its critical
behavior. Its goals are to give an account of the current
mathematical understanding of the model, to indicate some of the
applications of the concept in physics and in chemistry, and to
give an introduction to some of the nonrigorous methods used in
those fields.
Topics covered in the bookinclude: the lace expansion and its
application to the self-avoiding walk in more than four dimensions
where most issues are now resolved; an introduction to the
nonrigorous scaling theory; classical work of Hammersley and
others; a new exposition of Kesten s pattern theorem and its
consequences; a discussion of the decay of the two-point function
and its relation to probabilistic renewal theory; analysis of Monte
Carlo methods that have been used to study the self-avoiding walk;
the role of the self-avoiding walk in physical and chemical
applications. Methods from combinatorics, probability theory,
analysis, and mathematical physics play important roles. The book
is highly accessible to both professionals and graduate students in
mathematics, physics, and chemistry.
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