{"id":"openai-math/Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights","pdf":"https://github.com/openai/math/blob/main/preprints/Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights-October-6-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Gaussian-free-field-limits-of-weighted-integer-Lipschitz-heights-October-6-2026","tags":["gaussian-free-field","statistical-mechanics","probability"],"score":0,"title":"Gaussian free-field limits of weighted integer Lipschitz heights","domain":"Probability and statistical mechanics","family":"232","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove a Gaussian free field scaling limit for weighted integer Lipschitz heights on the triangular lattice. With zero boundary values and a factor x for each edge on which the height changes, the field converges after division by a positive constant depending only on x to the zero-Dirichlet Gaussian free field, for every fixed $`x\\in[1/\\sqrt2,1]`$. The convergence holds as a random distribution on every bounded C 2 Jordan domain under inside lattice approximations with uniformly convergent boundary parametrizations. This includes the uniform height model and the predicted critical endpoint.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"Gaussian fields and interfaces for triangular-lattice Lipschitz heights"}