---
res:
  bibo_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. The scaling of the correlation length of the latter
    was recently characterized in Probab. Duke Math. J. 172(9), 1781–1811 (2023) and
    arXiv:2011.08768v3, (2022); our analysis is reminiscent of the multi-scale approach
    of the latter work and of Combinatorica 9, 161–187 (1989) . 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. We also establish a quenched
    homogenization result in the sense that the leading order of the minimal energy
    becomes deterministic as the ratio system size / lattice spacing diverges. To
    this purpose we adapt arguments from arXiv:2401.06768, (2024) on the (d + 1)-dimensional
    version our the model, with a Brownian replacing the white noise potential, to
    obtain the initial large-scale bounds. Based on our estimate of the (p = 3)-Dirichlet
    energy, we give an informal justification of the geometric linearization. Our
    bounds, which are oblivious to the microscopic cut-off scale provided by the lattice
    spacing, yield tightness of the law of minimizers in the space of continuous functions
    as the lattice spacing is sent to zero.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Felix
      foaf_name: Otto, Felix
      foaf_surname: Otto
  - foaf_Person:
      foaf_givenName: Matteo
      foaf_name: Palmieri, Matteo
      foaf_surname: Palmieri
  - foaf_Person:
      foaf_givenName: Christian
      foaf_name: Wagner, Christian
      foaf_surname: Wagner
      foaf_workInfoHomepage: http://www.librecat.org/personId=bf0c729b-2619-11f0-8024-9d69bb2b8b20
  bibo_doi: 10.1007/s00440-026-01468-y
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0178-8051
  - http://id.crossref.org/issn/1432-2064
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: On minimizing curves in a Brownian potential@
...