Author

Felix Otto

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Preprint Sep 2026

Asymptotics of a planar isoperimetric problem with a white-noise volume term

In this work we study the maximal ratio $I$ between the white noise integrated over a set and the perimeter of the set, which can be seen as a random isoperimetric problem, and appears in the random-field Ising model (Ding-Wirth) and min-max optimal matching (Leighton-Shor). In the planar case considered here, such a r...

Xiao-Peng Cheng, Felix Otto, Matteo Palmieri · 2 citations

Preprint Sep 2026

A geometrically linear approximation of min-max optimal matching

In this work we establish a connection between the min-max optimal matching in the critical dimension $d=2$ and a simpler, geometrically linear, action of random curves in a Brownian potential. This is done by following Leighton and Shor and working with the dual formulation, which we approximate by a problem of isoper...

Xiao-Peng Cheng, Felix Otto, Matteo Palmieri et al. · 2 citations