A probabilistic analogue of the Fourier extension conjecture

Abstract: We prove a probabilistic Fourier extension theorem that says Fourier extension holds when averaged over certain smooth Alpert multipliers. The proofs use smooth Alpert wavelets with the classical techniques of stationary phase and interpolation of L^2 and L^4 estimates. The correct L^4 bounds for resonant forms require an expectation over Alpert multipliers.