{"schema":"vela.problem-packet.v0.1","problem":529,"statement":"Let $d_k(n)$ be the expected distance from the origin after taking $n$ random steps from the origin in $\\mathbb{Z}^k$ (conditional on no self intersections) - that is, a self-avoiding walk. Is it true that\\[\\lim_{n\\to \\infty}\\frac{d_2(n)}{n^{1/2}}= \\infty?\\]Is it true that\\[d_k(n)\\ll n^{1/2}\\]for $k\\geq 3$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}