  We study the leading corrections to the emergent canonical commutation
relations arising in the statistical mechanics of matrix models, by deriving
several related Ward identities, and give conditions for these corrections to
be small. We show that emergent canonical commutators are possible only in
matrix models in complex Hilbert space for which the numbers of fermionic and
bosonic fundamental degrees of freedom are equal, suggesting that supersymmetry
will play a crucial role. Our results simplify, and sharpen, those obtained
earlier by Adler and Millard.
