  We consider the asymptotic distribution of the IP sparsity function, which
measures the minimal support of optimal IP solutions, and the IP to LP distance
function, which measures the distance between optimal IP and LP solutions. We
create a framework for studying the asymptotic distribution of general
functions related to integer optimization. There has been a significant amount
of research focused around the extreme values that these functions can attain,
however less is known about their typical values. Each of these functions is
defined for a fixed constraint matrix and objective vector while the right hand
sides are treated as input. We show that the typical values of these functions
are smaller than the known worst case bounds by providing a spectrum of
probability-like results that govern their overall asymptotic distributions.
