  We generalize QCD at asymptotically large isospin chemical potential to an
arbitrary even number of flavors. We also allow for small quark chemical
potentials, which stress the coincident Fermi surfaces of the paired quarks and
lead to a sign problem in Monte Carlo simulations. We derive the corresponding
low-energy effective theory in both $p$- and $\epsilon$-expansion and quantify
the severity of the sign problem. We construct the random matrix theory
describing our physical situation and show that it can be mapped to a known
random matrix theory at low baryon density so that new insights can be gained
without additional calculations. In particular, we explain the Silver Blaze
phenomenon at high isospin density. We also introduce stressed singular values
of the Dirac operator and relate them to the pionic condensate. Finally we
comment on extensions of our work to two-color QCD.
