Total Variation for the Lamplighter Walk on Z

For the switch-walk-switch walk on $\mathbb{Z}_2 \wr \mathbb{Z}$ started at $(0,0)$ and $(0,2)$, prove $\|P_t^x - P_t^y\|_{TV} \asymp t^{-1/2}$.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Probability on groups

Posed by

—

Year posed

2025

Years open

1y

Solved

2026-05-15

Model

QED (GPT-5.5)

Vendor

OpenAI

Collaborators

—

Verification

Independently expert-verified

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article