Random flag complexes and asymptotic syzygies

Abstract

We use the probabilistic method to construct examples of conjectured phenomena about asymptotic syzygies. In particular, we use Stanley–Reisner ideals of random flag complexes to construct new examples of Ein and Lazarsfeld’s nonvanishing for asymptotic syzygies and of Ein, Erman, and Lazarsfeld’s conjecture on how asymptotic Betti numbers behave like binomial coefficients.