Universality conjectures for random knot models

Let $K_n$ be a random knot sampled from the Random Jump, Petaluma, or Grid model. Random-knot universality conjectures. The following properties are expected: with high probability $K_n$ is prime, and even hyperbolic; with high probability $K_n$ is non-alternating; $E[c(K_n)]=\omega(n)$; for every knot $K$, $P[K_n=K]=e^{-\omega(n)}$; and every finite type invariant of order $m$ has typical order of magnitude $n^m$. These are listed as desired features of the models and remain to be established in the supplied context.