“Computing Extreme Values of Continuous & Discrete Fractional Gaussian Fields on Manifolds” by Tyler Campos (Yale & UConn REU 2022) and Connor Marrs (Bowdoin & UConn REU 2022)

Fractional Gaussian Fields (FGF’s) are a family of stochastic processes that can be defined on any compact manifold M and model the behavior of random oscillations on M. FGF’s can be used to model for the behavior of bosons in particle physics, but they also find use in exploiting the connection between random matrix theory and number theory to prove the Riemann Hypothesis. For these reasons, studying the extreme values of these fields is of great interest to a variety of subjects, and yet computing the distributions of the maxima and minima of the FGF are challenging, open problems. We define discrete fractional gaussian fields on manifolds M that converge to the continuous fractional field, and by numerically simulating the discrete fractional gaussian fields, we generate conjectures for the behavior of the extreme values of the continuous field.

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