Dear Colleagues,

We would like to invite you to the following SPASS seminar,

On minimizing curves in a Brownian potential

by Matteo Palmieri (Max Planck Inst. Lepzig),

WED 19.11.2025 at 14:00 CET in Saletta Riunioni, Dipartimento di Matematica, UNIPI.

Best,

Francesco Grotto on behalf of the organizers

 https://sites.google.com/unipi.it/spass 

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Abstract: We study a (1+1)-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model (at zero temperature). We show that at every dyadic scale from the system size down to the lattice spacing the minimizer contains at most order-one Dirichlet energy per unit length, leading to a logarithmic scaling of the minimal energy. Using super-additivity in the scales, this allows us to establish a quenched homogenization result in the sense that he leading order of the minimal energy becomes deterministic as the ratio system size/lattice spacing diverges. This is joint work with Felix Otto and Christian Wagner.