  The Langmann-Szabo-Zarembo (LSZ) matrix model is a complex matrix model with
a quartic interaction and two external matrices. The model appears in the study
of a scalar field theory on the non-commutative plane. We prove that the LSZ
matrix model computes the probability of atypically large fluctuations in the
Stieltjes-Wigert matrix model, which is a $q$-ensemble describing $U(N)$
Chern-Simons theory on the three-sphere. The correspondence holds in a
generalized sense: depending on the spectra of the two external matrices, the
LSZ matrix model either describes probabilities of large fluctuations in the
Chern-Simons partition function, in the unknot invariant or in the two-unknot
invariant. We extend the result to supermatrix models, and show that a
generalized LSZ supermatrix model describes the probability of atypically large
fluctuations in the ABJ(M) matrix model.
