A Gaussian Kinematic Formula

@inproceedings{Taylor2003AGK,
  title={A Gaussian Kinematic Formula},
  author={Jonathan E. Taylor},
  year={2003}
}
In this paper, we consider smooth, real-valued random fields built up from i.i.d. copies of centered, unit variance smooth Gaussian fields on a manifold M . Specifically, we consider random fields of the form fp = F (y1(p), . . . , yk(p)) for F ∈ C(R; R) and (y1, . . . , yk) a vector of C centered, unit-variance Gaussian fields. For fields of this type, we compute the expected Euler characteristic, χ, of the excursion sets f−1[u,+∞) in terms of geometric quantities related to the Riemannian… CONTINUE READING
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