Conjecture on the limiting expected volume per crossing of random alternating link diagrams

Let $\mathit{Vol}_n$ denote the hyperbolic volume of a random alternating link diagram with $n$ crossings, and let $\mathbb{E}[\mathit{Vol}_n]$ be its expectation. Limiting expected-volume conjecture. The expectation of the hyperbolic volume per crossing,

$$\frac{1}{n}\mathbb{E}[\mathit{Vol}_n]$$

converges to a limiting value as $n\to\infty$. The preceding bounds show that the expected volume grows linearly up to lower-order terms, but convergence of the expected volume per crossing is unknown.