  A Gaussian approximation to the bosonic part of M-(atrix) theory with mass
deformation is considered at large values of the dimension $d$. From the
perspective of the gauge/gravity duality this action reproduces with great
accuracy the stringy Hagedorn phase transition from a confinement (black
string) phase to a deconfinement (black hole) phase whereas from the
perspective of the matrix/geometry approach this action only captures a remnant
of the geometric Yang-Mills-to-fuzzy-sphere phase where the fuzzy sphere
solution is only manifested as a three-cut configuration termed the "baby fuzzy
sphere" configuration. The Yang-Mills phase retains most of its characteristics
with two exceptions: i) the uniform distribution inside a solid ball suffers a
crossover at very small values of the gauge coupling constant to a Wigner's
semi-circle law, and ii) the uniform distribution at small values of the
temperatures is non-existent.
