The curious asymptotics of 3-sided prudent polygons
Presented by Prof. Anthony J GUTTMANN
Type: Oral presentation
Track: General session
In joint work with Nick Beaton (PhD student) and Philippe Flajolet, we have studied a range of solvable self-avoiding walk and polygon models. One of these, the so-called 3-sided prudent polygons, enumerated by area, displays quite unexpected asymptotics. Writing the dominant asymptotic form of the coefficients as $a_n \sim A \times \mu^n \times n^g,$ we find $g$ to be irrational, and more surprisingly, $A$ does not exist, due to the presence of long-period, small amplitude oscillatory component. We discuss this model and other models in this family.