Statistics of thawing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -essence dark energy models

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