  In this article we study the tail probability of the mass of Gaussian
multiplicative chaos. With the novel use of a Tauberian argument and Goldie's
implicit renewal theorem, we provide a unified approach to general
log-correlated Gaussian fields in arbitrary dimension and derive precise first
order asymptotics of the tail probability, resolving a conjecture of Rhodes and
Vargas. The leading order is described by a universal constant that captures
the generic property of Gaussian multiplicative chaos, and may be seen as the
analogue of the Liouville unit volume reflection coefficients in higher
dimensions.
