5 problems

Alexander-invariant limit conjecture. For $t=-1$ (respectively, $t=i$), there exist numbers $c_t$, $\gamma_t$, and $\alpha_t$ such that the sequence of random variables

Let $\Gamma$ be the interface curve joining opposite corners of a three-dimensional cube of size $N$, and let $L_N$ be its length, defined as the number of tetrahedra crossed by th…

In dimension $3$, let $K^\text{Arm}(n,w,k,r)$ be the probability that a length-$k$ arc of a random open arm is an $r$-local knot, and let $K^\text{Pol}(n,w,k,r)$ be the correspondi…

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…

Let $T(3,n+1)$ be the random knot model obtained from Chebyshev billiard table diagrams, and let $P(T^{(n)}_K)$ denote the probability that the resulting diagram represents a fixed…