For the relationship between concentration of the measure and this: the main theorems of concentration generalise the CLT beyond the additive case, for any lipschitz operator over iid vars, the first i can even be relaxed.
You can find online, works by eg. Gromov and his students for a deeper understanding.
For the relationship between concentration of the measure and this: the main theorems of concentration generalise the CLT beyond the additive case, for any lipschitz operator over iid vars, the first i can even be relaxed.
You can find online, works by eg. Gromov and his students for a deeper understanding.