  Negative, or latent, dimensions have always attracted a strong interest since
their discovery. When randomness is introduced in multifractals, the
sample-to-sample fluctuations of multifractal spectra emerge inevitably, which
has motivated various studies in this field. In this work, we study a class of
multinomial measures and argue the asymptotic behaviors of the multifractal
function as . The so-called latent dimensions condition (LDC) is presented
which states that latent dimensions may be absent in discrete random
multinomial measures. In order to clarify the discovery, several examples are
illustrated.
