Olof Sisask co-developed the Croot-Sisask almost-periodicity theorem with Ernie Croot, introducing a probabilistic method for finding almost-periods of convolutions in additive combinatorics.[ref]
Their proof approximates a convolution by sampling and then looks for translations preserving the approximation. Norm estimates turn that probabilistic approximation into many approximate symmetries. The method provides a way to detect additive structure without requiring exact periodicity.[ref]
A probabilistic technique for finding almost-periods of convolutions by Ernie Croot and Olof Sisask. Section 3, sampling proof
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