The lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks (Q5943922)
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scientific article; zbMATH DE number 1648748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks |
scientific article; zbMATH DE number 1648748 |
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The lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks (English)
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21 October 2002
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The author proves ballistic behaviour for a one-dimensional model of weakly self-avoiding walk. It is proved that the fluctuations around the linear drift satisfy a central limit theorem, and a law of large numbers is derived. The proof uses a variant of the lace expansion (which behaviour is not diffusive) and an inductive analysis of the arising recursion relation. A comparison with the strictly self-avoiding walk is made.
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weakly self-avoiding walk
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central limit theorem
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law of large numbers
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lace expansion
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induction
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