Spectral Gap

The positive separation in the spectrum of a linear operator (or transition operator) between the dominant spectral value controlling the steady state and the remainder of the spectrum; it quantifies the slowest nontrivial relaxation rate to equilibrium.

The difference between distinguished parts of the spectrum of a linear operator or matrix, commonly the gap between the dominant spectral value(s) and the remainder (for example, the difference between the largest and second-largest eigenvalues in modulus or real part).

A positive lower bound in the spectrum of a linear operator that separates a distinguished part of the spectrum (often the ground state or the eigenvalue 0) from the remainder: there exists ε>0 so that no spectral value lies in (0,ε).