论文标题
自我避免步行和局限于正方形的多边形
Self-avoiding walks and polygons confined to a square
论文作者
论文摘要
我们证明了关于多边形数量和避免自我的步行的渐近行为的严格结果，仅限于正方形的正方形。具体而言，我们证明，局限于LXL正方形的多边形的主要渐近行为与从一个角顶点到另一个角顶点的LXL正方形越过LXL正方形的自我避免行走相同。我们还证明了关于避开正方形的自避免步行的亚抑制渐近行为的结果，并将其扩展到局限于正方形的多边形。此外，我们研究了D维超维超纤维晶格中超立方体中自我避免行走和多边形的问题。
We prove several rigorous results about the asymptotic behaviour of the numbers of polygons and self-avoiding walks confined to a square on the square lattice. Specifically we prove that the dominant asymptotic behaviour of polygons confined to an LxL square is identical to that of self-avoiding walks that cross an LxL square from one corner vertex to the opposite corner vertex. We also prove a result about the subdominant asymptotic behaviour of self-avoiding walks crossing a square and extend this result to polygons confined to a square. In addition, we investigate the problems of self-avoiding walks and polygons in a hypercube in the d-dimensional hypercubic lattice.
