Asymptotic normality of pattern counts in random maps II
This work addresses theoretical problems in combinatorics and probability for researchers studying random maps, but it is incremental as it builds on prior results with a more efficient proof.
The paper provides a shorter proof for the asymptotic normality of pattern counts in random planar maps by computing bivariate coefficient asymptotics from a functional equation, extending the result to pattern counts with arbitrary boundary and new map classes.
In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate coefficient asymptotics from a functional equation with one catalytic variable and extend the result to pattern counts with arbitrary boundary and new map classes.