7 problems

Airy scaling conjecture. The pressure-induced phase transition is characterized by a tri-critical point, and the associated single-variable scaling function is given by the logarit…

Let $r\ge1$ and $s\ge2$ be given. For staircase polygons and rooted self-avoiding polygons, let $F^{(r,s)}(z)$ and $F^{(r)}(z)$ be the corresponding area amplitude series. Suppose…

Let $r\ge1$ be the number of punctures and let $s\ge2$ denote the relevant perimeter parameter for punctured staircase polygons. Let $F^{(r,s)}(z)$ be their area amplitude series,…

Self-avoiding polygon Airy conjecture. The derivative of the scaling function is

Wu's scaling-function constant conjecture. The numerical constant in the leading term is

Elliptic reproduction conjecture. In the case of not scale-invariant differential operators, the corresponding elliptic scaling functions reproduce not scale-invariant polynomial s…

For self-avoiding polygons, let $F(s)$ be the scaling function in the tricritical scaling form near $(x_c,1)$, and let $x_c$ and $A_0$ denote the constants appearing in that scalin…