Asymptotic volume–determinant conjecture for knots

Let $K$ be a knot, let $\det(K)$ denote its determinant, let $\operatorname{Vol}(K)$ denote its hyperbolic volume, and let $c$ denote the crossing number. Asymptotic volume–determinant conjecture. There exist constants $a,b\in\mathbb{R}$ such that the percentage of knots for which

$$\log\det(K)<a\cdot\operatorname{Vol}(K)+b$$

converges to $1$ as $c\to\infty$. The corresponding assertion for every knot is false because twist and pretzel-knot families can have bounded volume and unbounded determinant; the conjecture retains the proposed inequality only in the asymptotic-density sense.