Inside the critical window for cohomology of random k-complexes

@article{Kahle2016InsideTC,
  title={Inside the critical window for cohomology of random k-complexes},
  author={Matthew Kahle and B. Pittel},
  journal={Random Struct. Algorithms},
  year={2016},
  volume={48},
  pages={102-124}
}
We prove sharper versions of theorems of Linial–Meshulam and Meshulam–Wallach which describe the behavior for -cohomology of a random k-dimensional simplicial complex within a narrow transition window. In particular, we show that if Y is a random k-dimensional simplicial complex with each k-simplex appearing i.i.d. with probability with and fixed, then the dimension of cohomology is asymptotically Poisson distributed with mean . In the k = 2 case we also prove that in an… Expand
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