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For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues arescattered in the complex plane. We define a notion of ordering for individualeigenvalues in this case and derive the distributions of individual eigenvaluesfrom random matrix theory (RMT). We distinguish two cases depending on theparameter $\alpha=\mu^2 F^2 V$, where $V$ is the volume and $F$ is the familiarlow-energy constant of chiral perturbation theory. For small $\alpha$, we use aFredholm determinant expansion and observe that already the first few termsgive an excellent approximation. For large $\alpha$, all spectral correlationsare rotationally invariant, and exact results can be derived. We compare theRMT predictions to lattice data and in both cases find excellent agreement inthe topological sectors $\nu=0,1,2$.

Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results