  We verify that the eigenstate thermalization hypothesis (ETH) holds
universally for locally interacting quantum many-body systems. Introducing
random-matrix ensembles with interactions, we numerically obtain a distribution
of maximum fluctuations of eigenstate expectation values for different
realizations of the interactions. This distribution, which cannot be obtained
from the conventional random matrix theory involving nonlocal correlations,
demonstrates that an overwhelming majority of pairs of local Hamiltonians and
observables satisfy the ETH with exponentially small fluctuations. The
ergodicity of our random matrix ensembles breaks down due to locality.
