4 problems

Self-avoiding loop scaling-limit conjecture.

Finite-reinforcement percolation conjecture. Assume that $d=k=2$. Then there exists $\alpha_0>0$ such that

Percolation conjecture for $d=k=2$. Assume that $d=k=2$. Then

Let $x \in \mathbb{Z}^2$ be a neighbor of the origin, and let $p_N$ be the probability that $x$ lies on the loop-erased random walk from $o$ to $\partial G_N$. Loop-erased random w…