  We prove a local gap theorem for Ricci shrinkers, which states that if the
local $\mu$-functional at scale $1$ on a large ball centered at the minimum
point of the potential function is close enough to $0$, then the shrinker must
be the flat gaussian shrinker. In relation to our result, Yokota [Yo09,Yo12]
proved the same result assuming the global $\mu$-functional to be close enough
to $0$. Our result shows an aspect of how the local geometry of a shrinker
controls the global geometry, which is also discussed in [LW19,LW20,LW21].
