Question

Bonus problem: Influence of recursive majority Recall that in the lecture we proved Inf1 [Majn] ~ ?2/?1/n, that is, the influence of majority asymptotically decreases to zero with the speed proportional to ?1/n. The task is to perform a similar calculation for the level-two majority. That is, let Maj 2: {±1} ? {±1} be the level-two majority defined for all n such that n = m² for some m odd. Find an explicit sequence (an) such that Inf1 [Maj 2] ~ an, in other words such that \lim_{n \to \infty} \frac{\text{Inf1} [\text{Maj}_n^{\otimes 2}]}{a_n} = 1. The deadline for the bonus problem only is Friday, June 23. It is a bonus problem and it will be marked strictly.

          Bonus problem: Influence of recursive majority
Recall that in the lecture we proved Inf1 [Majn] ~ ?2/?1/n, that is, the influence of majority asymptotically decreases
to zero with the speed proportional to ?1/n.
The task is to perform a similar calculation for the level-two majority. That is, let Maj 2: {±1} ? {±1} be
the level-two majority defined for all n such that n = m² for some m odd. Find an explicit sequence (an) such that
Inf1 [Maj 2] ~ an, in other words such that
\lim_{n \to \infty} \frac{\text{Inf1} [\text{Maj}_n^{\otimes 2}]}{a_n} = 1.
The deadline for the bonus problem only is Friday, June 23. It is a bonus problem and it will be
marked strictly.

Bonus problem: Influence of recursive majority
Recall that in the lecture we proved Inf1 [Majn] ?2/?1/n, that is, the influence of majority asymptotically decreases
to zero with the speed proportional to ?1/n.
The task is to perform a similar calculation for the level-two majority. That is, let Maj 2: ±1 ? ±1 be
the level-two majority defined for all n such that n = m² for some m odd. Find an explicit sequence (an) such that
Inf1 [Maj 2] an, in other words such that
limn →∞ (Inf1 [Majn^⊗2])/(an) = 1.
The deadline for the bonus problem only is Friday, June 23. It is a bonus problem and it will be
marked strictly.

Added by Edwin M.

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