Generalised Atmospheric Rosenbluth Methods (GARM)

TL;DR

This paper introduces a generalized atmospheric Rosenbluth method (GARM) that extends classical sampling techniques to a broader class of combinatorial objects like self-avoiding walks and polygons, enhancing sampling flexibility.

Contribution

The paper develops a new generalized algorithm for sampling complex objects, incorporating flexible moves and combining pruning, enrichment, and length-preserving transformations.

Findings

Effective sampling of self-avoiding walks and polygons achieved

Algorithm can be combined with pivot and crank-shaft moves

Enhanced sampling efficiency demonstrated

Abstract

We show that the classical Rosenbluth method for sampling self-avoiding walks can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons. The implementation relies on an elementary move which is a generalisation of kinetic growth; rather than only appending edges to the endpoint, edges may be inserted at any vertex providing the resulting objects still lie within the same family. We implement this method using pruning and enrichment to sample self-avoiding walks and polygons. The algorithm can be further extended by mixing it with length-preserving moves, such pivots and crank-shaft moves.