Abstract
In this chapter we consider the same model as in Chapter 3, but for d ? 5 instead of d = 1. Our goal is to prove diffusive behavior. The tool to achieve this is the so-called lace expansion, a combinatorial technique that hinges on the idea that in high dimensions the soft polymer can be viewed as a “perturbation” of SRW. For the exposition below, we borrow from van der Hofstad [156], Section 2, and Slade [280], Chapter 3. Figs. 4.2-4.4 are borrowed from Gordon Slade, Fig. 4.5 from Bill Casselman and Gordon Slade.
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© 2009 Springer-Verlag Berlin Heidelberg
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Hollander, F.d. (2009). Soft Polymers in High Dimension. In: Random Polymers. Lecture Notes in Mathematics(), vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00333-2_4
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DOI: https://doi.org/10.1007/978-3-642-00333-2_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00332-5
Online ISBN: 978-3-642-00333-2
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