  We explore the conjectured duality between a class of large $N$ matrix
integrals, known as multicritical matrix integrals (MMI), and the series
$(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match
the critical exponents of the leading order planar expansion of MMI, to those
of the continuum theory on an $S^2$ topology. From the MMI perspective this is
done both through a multi-vertex diagrammatic expansion, thereby revealing
novel combinatorial expressions, as well as through a systematic saddle point
evaluation of the matrix integral as a function of its parameters. From the
continuum point of view the corresponding critical exponents are obtained upon
computing the partition function in the presence of a given conformal primary.
Further to this, we elaborate on a Hilbert space of the continuum theory, and
the putative finiteness thereof, on both an $S^2$ and a $T^2$ topology using
BRST cohomology considerations. Matrix integrals support this finiteness.
