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Loop-erased random walk

In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. It is a case of the more general topic of random walks.

Products, Grids & The Laplacian random walk

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Overview

Definition

Uniform spanning tree

The Laplacian random walk

Grids

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Map overview Semantic statistics

Loop-erased random walk

Nodes48
Edges47
Triples113
Avg. degree1.96
Density0.041667
Components1

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Loop-erased random walk

Top relations

related to References · 78
Loop-erased random walk → Acta Mathematica, Andrei, Annals, Applications, April, Association, BF02392811Kenyon, BF02803524Wilson, Bibcode, Birkhäuser, Boston, Bramson, Choosing, Computing, Computing Machinery, Conference, Conformal, David Bruce, Duke Mathematical Journal, Durrett
related to Uniform spanning tree · 7
Loop-erased random walk → First, For, Repeating, The, Then, There, Wilson's
related to High dimensions · 6
Loop-erased random walk → Brownian, Dimension, In, It, Scaling, The
related to The Laplacian random walk · 6
Loop-erased random walk → Another, Assume, Construct, Laplace, Let, Where
related to Two dimensions · 6
Loop-erased random walk → Assume, Examine, In, Let, Take, Then
related to Three dimensions · 5
Loop-erased random walk → Hausdorff, If, Numerical, The, This
related to Grids · 4
Loop-erased random walk → Examine Zd, From, Let, This
is a · 1
Loop-erased random walk → model for a random simple path with important applications in combinatorics

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Important terminology

random walk loop-erased path displaystyle tree graph spanning gamma vertices uniform simple connected scaling dimensions domino doi length one starting

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Loop-erased random walkis amodel for a random simple path with important applications in combinatorics0.90text
Loop-erased random walkrelated to GridsLet0.60section
Loop-erased random walkrelated to GridsExamine Zd0.60section
Loop-erased random walkrelated to GridsThis0.60section
Loop-erased random walkrelated to GridsFrom0.60section
Loop-erased random walkrelated to High dimensionsThe0.60section
Loop-erased random walkrelated to High dimensionsIn0.60section
Loop-erased random walkrelated to High dimensionsScaling0.60section
Loop-erased random walkrelated to High dimensionsBrownian0.60section
Loop-erased random walkrelated to High dimensionsDimension0.60section
Loop-erased random walkrelated to High dimensionsIt0.60section
Loop-erased random walkrelated to ReferencesLock-green0.60section

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