  We report calculations of the density of maximally random jamming (aka random
close packing) of one-component and binary hard disc fluids. The theoretical
structure used provides a common framework for description of the hard disc
liquid to hexatic, the liquid to hexagonal crystal and the liquid-to-maximally
random jammed state transitions. Our analysis is based on locating a particular
bifurcation of the solutions of the integral equation for the inhomogeneous
single particle density at the transition between different spatial structures.
The bifurcation of solutions we study is initiated from the dense metastable
fluid, and we associate it with the limit of stability of the fluid, which we
identify with the transition from the metastable fluid to a maximally random
jammed state. For the one-component hard disc fluid the predicted packing
fraction at which the metastable fluid to maximally random jammed state
transition occurs is 0.84, in excellent agreement with the experimental value
0.84 \pm 0.02. The corresponding analysis of the limit of stability of a binary
hard disc fluid with specified disc diameter ratio and disc composition
requires extra approximations in the representations of the direct correlation
function, the equation of state, and the number of order parameters accounted
for. Keeping only the order parameter identified with the largest peak in the
structure factor of the highest density regular lattice with the same disc
diameter ratio and disc composition as the binary fluid, the predicted density
of maximally random jamming is found to be 0.84 to 0.87, depending on the
equation of state used, and very weakly dependent on the ratio of disc
diameters and the fluid composition, in agreement with both experimental data
and computer simulation data.
