Some New Self-Avoiding Walk And Polygon Models

We study the behaviour of prudent, perimeter and quasi-prudent self-avoiding walks and polygons in both two and three dimensions, as well as some solvable subsets. Our analysis combines exact solutions of some simpler cases, careful asymptotic analysis of functional equations which can be obtained in more complicated cases and extensive numerical studies based on exact series expansions for less tractable cases, augmented by long Monte Carlo runs in some cases.