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We investigate certain families X~, 0 < ~ 1, of Gaussian random smooth functions on the m-dimensional torus T~ := Rm/(~−1Z)m. We show that for any cube B ⊂ R… Click to show full abstract
We investigate certain families X~, 0 < ~ 1, of Gaussian random smooth functions on the m-dimensional torus T~ := Rm/(~−1Z)m. We show that for any cube B ⊂ R of size < 1/2 and centered at the origin, the number of critical points of X~ in the region ~−1B/(~−1Z)m ⊂ T~ has mean ∼ c1~, variance ∼ c2~, c1, c2 > 0, and satisfies a central limit theorem as ~↘ 0.
Keywords:
random fourier;
points multidimensional;
critical points;
series central;
fourier series;
multidimensional random
Journal Title: Bernoulli
Year Published: 2018
Link to full text (if available)
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Journal Title: Bernoulli
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!