Abstract: In this talk, we study the random 3-manifolds with a Heegaard splitting of fixed genus $g\ge 2$, under a geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a random Heegaard splitting increases linearly to the infinity. In particular, random 3-manifolds are hyperbolic in the Teichmuller model. This is ongoing work with Suzhen Han and Yanqing Zou.
