Schramm's Problem 2.3: Gaussian free field and SLE limits of uniform real Lipschitz heights on the triangular lattice
Principal manuscript: on approximations of smooth simply connected domains, the centered uniform real Lipschitz height converges as a random distribution to a multiple of the Dirichlet GFF, and at one tuned amplitude the zero-height interface converges in uniform curve distance to chordal SLE; the variance-boundary relation is given through an implicit coefficient, so constants are not explicit. Companion: the field part of Problem 2.2 (uniform odd integer heights, boundary ) with an absolutely convergent normalization formula; the Problem 2.2 interface is not proved. Companion: GFF limits for zero-boundary integer Lipschitz heights weighted by (loop ), part of a conjecture discussed by Glazman and Lammers; larger is not covered.
Exact FrontierDelta
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Occurred: Sep 25, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Schramm's Problem 2.3: Gaussian free field and SLE$_4$ limits of uniform real Lipschitz heights on the triangular lattice · Schramm's Problem 2.3: real Lipschitz heights
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
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Schramm's Problem 2.3: Gaussian free field and SLE limits of uniform real Lipschitz heights on the triangular lattice evidence for this event
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Principal manuscript: on approximations of smooth simply connected domains, the centered uniform real Lipschitz height converges as a random distribution to a multiple of the Dirichlet GFF, and at one tuned amplitude the zero-height interface converges in uniform curve distance to chordal SLE; the variance-boundary relation is given through an implicit coefficient, so constants are not explicit. Companion: the field part of Problem 2.2 (uniform odd integer heights, boundary ) with an absolutely convergent normalization formula; the Problem 2.2 interface is not proved. Companion: GFF limits for zero-boundary integer Lipschitz heights weighted by (loop ), part of a conjecture discussed by Glazman and Lammers; larger is not covered. parent of this event
Schramm's Problem 2.3: Gaussian free field and SLE limits of uniform real Lipschitz heights on the triangular lattice parent of this event
Schramm, Conformally invariant scaling limits: an overview and a collection of problems (ICM 2006) evidence for this event
Revised edition (October 6, 2026): The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data evidence for this event
Companion: Gaussian free-field limits of weighted integer Lipschitz heights evidence for this event
Companion: The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data evidence for this event
VibeMathed record: Schramm's Problem 2.3: Gaussian free field and SLE limits of uniform real Lipschitz heights on the triangular lattice evidence for this event
Earlier edition (September 25, 2026) evidence for this event
Revised edition (October 6, 2026): Gaussian free-field limits of weighted integer Lipschitz heights evidence for this event
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