Fluctuations of the Euler-Poincar\'e characteristic for random spherical harmonics
classification
🧮 math.PR
math-phmath.MP
keywords
characteristiceuler-poincarasymptoticbuildeigenfunctionsexcursionexpressionfluctuations
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In this short note, we build upon some recent results to present a precise expression for the asymptotic variance of the Euler-Poincar\'e characteristic for the excursion sets of Gaussian eigenfunctions on ${\cal S}^2$.
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