3 problems

Consider the generic prudent walk at $\beta=0$. For the three-sided prudent walk, the scaling limit is a straight line along the diagonal. Generic prudent-walk diagonal scaling con…

Let $G(x)$ be the generating function for unrestricted prudent walks. A generating function is D-finite if it satisfies a linear differential equation with polynomial coefficients.…

Let $G(x)$ be the length-generating function for unrestricted prudent walks, and let $\rho=0.4030317168\ldots$ be the smallest real root of $1-2x-2x^2+2x^3$. Dethridge–Guttmann dom…