5 problems

Let $(W_n,G_n)$ be the barycentric excluded-volume random walk described in the paper, with $W_n\in\mathbb R^2$ its position, and let $\|\cdot\|$ denote Euclidean norm. Let…

Let $\beta>\beta_c$, and let $\widetilde\delta_c(\beta)$ be the wetting critical curve identified for the single-bead model. The unrestricted model has a collapsed phase…

Let $\beta>\beta_c$. In the collapsed phase, the lower envelope is described by a wetting model with critical point $\widetilde\delta_c(\beta)$. Sharp-asymptotics conjecture. For e…

Let $\beta_c$ denote the critical interaction parameter separating the extended and collapsed regimes, and let ${{\mathcal E}}$ be the extended phase. Critical-curve conjecture. Th…

A self-interacting walk in the collapsed phase ${{\mathcal C}}$ is decomposed into beads, which are much larger in ${{\mathcal C}}$ than in the extended phase. Unique macroscopic b…