Probabilistic Schubert calculus

@article{Brgisser2016ProbabilisticSC,
  title={Probabilistic Schubert calculus},
  author={Peter B{\"u}rgisser and A. Lerario},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year={2016},
  volume={2020},
  pages={1 - 58}
}
Abstract We initiate the study of average intersection theory in real Grassmannians. We define the expected degree edeg ⁡ G ⁢ ( k , n ) {\operatorname{edeg}G(k,n)} of the real Grassmannian G ⁢ ( k , n ) {G(k,n)} as the average number of real k-planes meeting nontrivially k ⁢ ( n - k ) {k(n-k)} random subspaces of ℝ n {\mathbb{R}^{n}} , all of dimension n - k {n-k} , where these subspaces are sampled uniformly and independently from G ⁢ ( n - k , n ) {G(n-k,n)} . We express edeg ⁡ G ⁢ ( k , n… Expand

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