Superlinear approximation of permutons by permutations occurs only when the permuton is supported on the graph of a measure-preserving function, with local regularity controlling the rate; the biased Brownian separable permuton has a positive lower bound on approximation error almost surely.
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On the approximation of permutons
Superlinear approximation of permutons by permutations occurs only when the permuton is supported on the graph of a measure-preserving function, with local regularity controlling the rate; the biased Brownian separable permuton has a positive lower bound on approximation error almost surely.