The genus of a random chord diagram is asymptotically normal

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 − log n ) / 2 for n → ∞ . We prove a local limit theorem for the distribution of G n , which implies that G n is asymptotically Gaussian, with mean ( n − log n ) / 2 and variance ( log n ) / 4 .