The genus of a random chord diagram is asymptotically normal

Abstract

Let $G_n$ be the genus of a two-dimensional surface obtained by gluing, uniformly at random, the sides of an $n$-gon. Recently Linial and Nowik proved, via an enumerational formula due to Harer and Zagier, that the expected value of $G_n$ is asymptotic to $(n-\ln n)/2$ for $n\to \infty$. We prove a local limit theorem for the distribution of $G_n$, which implies that $G_n$ is asymptotically Gaussian, with mean $(n-\ln n)/2$ and variance $(\ln n)/4$.

arXiv comment13 pages

References in corpus (1)

• The expected genus of a random chord diagram