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 $\|P_t^x - P_t^y\|_{TV} \asymp t^{-1/2}$.

10Significance / 100

1Frontier events

0Verification tasks

0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

probability-statisticsMay 15, 2026Significance 10/100Registry: expert verified

Prior state unknown→proved

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

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Source authenticated

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

Evidence graph

No public relationships recorded yet.