Editing Loop-erased random walk (section)

===Three dimensions===
The scaling limit exists and is invariant under rotations and dilations.<ref>{{harvtxt|Kozma|2007}}</ref> If <math>L(r)</math> denotes the expected number of vertices in the loop-erased random walk until it gets to a distance of ''r'', then

:<math>cr^{1+\varepsilon}\leq L(r)\leq Cr^{5/3}\,</math>

where ε, ''c'' and ''C'' are some positive numbers<ref>{{harvtxt|Lawler|1999}}</ref> (the numbers can, in principle, be calculated from the proofs, but the author did not do it). This suggests that the scaling limit should have Hausdorff dimension between <math>1+\varepsilon</math> and 5/3 almost surely. Numerical experiments show that it should be <math>1.62400\pm 0.00005</math>.<ref>{{harvtxt|Wilson|2010}}</ref>

{{more footnotes needed|date=June 2011}}