K-essence is a minimally-coupled scalar field whose Lagrangian density $mathcal{L}$ is a function of the field value $phi$ and the kinetic energy $X=frac{1}{2}partial_muphipartial^muphi$. In the thawing scenario, the scalar field is frozen by the large Hubble friction in the early universe, and therefore initial conditions are specified. We construct thawing k-essence models by generating Taylor expansion coefficients of $mathcal{L}(phi, X)$ from random matrices. From the ensemble of randomly generated thawing k-essence models, we select dark energy candidates by assuming negative pressure and non-growth of sub-horizon inhomogeneities. For each candidate model the dark energy equation of state function is fit to the Chevallier-Polarski-Linder parameterization $w(a) approx w_0+w_a(1-a)$, where $a$ is the scale factor. The thawing k-essence dark models distribute very non-uniformly in the $(w_0, w_a)$ space. About 90% models cluster in a narrow band in the proximity of a slow-roll line $w_aapprox -1.42 left(frac{Omega_m}{0.3}right)^{0.64}(1+w_0)$, where $Omega_m$ is the present matter density fraction. This work is a proof of concept that for a certain class of models very non-uniform theoretical prior on $(w_0, w_a)$ can be obtained to improve the statistics of model selection.
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