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Self-avoiding walk

In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding walk from a…

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Overview

Universality

Growing self-avoiding walk

Knots in self-avoiding polygons

On networks

Limits

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Map overview Semantic statistics

Self-avoiding walk

Nodes59
Edges58
Triples60
Avg. degree1.97
Density0.033898
Components1

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Self-avoiding walk

Top relations

related to Growing self-avoiding walk · 12
Self-avoiding walk → Flory, For, GSAW, GSAWs, However, On, SAW, SAWs, Snake, The, Thus, When
related to External links · 11
Self-avoiding walk → Also, Diamond, Eric, FiberWalks, Java, MathWorld, Norris, Number, OEISsequenceA007764, SAWs, Weisstein
related to On networks · 10
Self-avoiding walk → Erdős, For, Gompertz, In, It, Rényi, SAW, SAWs, Self-avoiding, The
related to Limits · 8
Self-avoiding walk → Consider, Harry Kesten, However, It, Loewner, One, Schramm, The
related to Universality · 8
Self-avoiding walk → Fekete's, Hugo Duminil-Copin, Let, One, Since, Stanislav Smirnov, The, Therefore
related to Knots in self-avoiding polygons · 6
Self-avoiding walk → As, It, On, SAP, Self-avoiding, The
is a · 1
Self-avoiding walk → chain-like path in R2 or R3 with a certain number of nodes

Important terminology Word statistics

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Important terminology

self-avoiding walk lattice length saws walks saw path number simulations volume probability average known believed step dimensions point excluded dimension

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Self-avoiding walkis achain-like path in R2 or R3 with a certain number of nodes0.90text
proteinsinstance ofthe SAW is believed to behave much like the ordinary random walk.SAWs and SAPs play a central role in the modeling of the topological and knot-theoretic behavior of thread- and…0.80text
solventsinstance ofin order to model the real-life behavior of chain-like entities0.80text
polymersinstance ofin order to model the real-life behavior of chain-like entities0.80text
whose physical volume prohibits multiple occupation of the same spatial point.SAWs are fractalsinstance ofin order to model the real-life behavior of chain-like entities0.80text
Self-avoiding walkrelated to External linksOEISsequenceA0077640.60section
Self-avoiding walkrelated to External linksNumber0.60section
Self-avoiding walkrelated to External linksAlso0.60section
Self-avoiding walkrelated to External linksWeisstein0.60section
Self-avoiding walkrelated to External linksEric0.60section
Self-avoiding walkrelated to External linksMathWorld0.60section
Self-avoiding walkrelated to External linksJava0.60section

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