Self-avoiding walk

SAWs and SAPs play a central role in the modeling of the topological and knot-theoretic behavior of thread- and loop-like molecules such as proteins.

Indeed, SAWs may have first been introduced by the chemist Paul Flory[1][dubious – discuss] in order to model the real-life behavior of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point.

The pivot algorithm is a common method for Markov chain Monte Carlo simulations for the uniform measure on n-step self-avoiding walks.

[3][4] One of the phenomena associated with self-avoiding walks and statistical physics models in general is the notion of universality, that is, independence of macroscopic observables from microscopic details, such as the choice of the lattice.

One important quantity that appears in conjectures for universal laws is the connective constant, defined as follows.

[7] In this context, it is customary to treat the SAW as a dynamical process, such that in every time-step a walker randomly hops between neighboring nodes of the network.

The walk ends when the walker reaches a dead-end state, such that it can no longer progress to newly un-visited nodes.