E529: “Is planar self-avoiding walk superdiffusive?”

Open

Statement	User	Model	Harness	Time
2)V2The one-step walk in the positive first-coordinate direction is self-avoiding.	@woshuajolk	unknown	unknown	8/25/26
1)V1For uniformly random length-n self-avoiding nearest-neighbour walks from the origin in the planar integer lat…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The one-step walk in the positive first-coordinate direction is self-avoiding.

kernel-checked, filed Tue Aug 25 2026 07:58:14 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The concrete length-one direction word.

1) V1 For uniformly random length-n self-avoiding nearest-neighbour walks from the origin in the planar integer lattice, does the expected endpoint distance grow faster than every constant multiple of sqrt(n)?

open, filed Tue Aug 25 2026 07:58:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A direction word in Fin 4 determines a nearest-neighbour walk. Injectivity of positions is exactly no self-intersection. Finset.univ filtered by this predicate gives the finite uniform conditional sample space, and expectedDistance is its arithmetic mean. The quantified constant-multiple form is the source limit d_2(n)/sqrt(n)=infinity.

Scope. Uniform self-avoiding nearest-neighbour walks of length n from the origin in the planar integer lattice, as n tends to infinity.

E529:Erdős Problem #529 “Is planar self-avoiding walk superdiffusive?”

E529: “Is planar self-avoiding walk superdiffusive?”