A lattice point counting approach for the study of the number of self-avoiding walks on $\mathbb{Z}^{d}$

Youssef Lazar

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arXiv · 2504.13093

A lattice point counting approach for the study of the number of self-avoiding walks on $\mathbb{Z}^{d}$

Youssef Lazar

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Abstract

We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length $n$ in the square lattice. This new formalism gives a natural and unified setting in order to study the properties of the number of self-avoiding walks in the lattice $\mathbb{Z}^{d}$ of any dimension $d\geq 2$.

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BibTeX RIS

Youssef Lazar. 2025-04-17. A lattice point counting approach for the study of the number of self-avoiding walks on $\mathbb{Z}^{d}$. https://arxiv.org/abs/2504.13093

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