{"id":"hexagon/2610.00347","pdf":"https://hexagonmath.org/pdf/2610.00347v1","url":"https://hexagonmath.org/abs/2610.00347v1","tags":["math.MG","msc:28A80","msc:28A78","msc:60E05","msc:43A62","Random matrices; fractals; hypergroups"],"score":0,"title":"Gaussian weights on fractals and Edelman's ghosts and shadows","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Djalil Chafaï"],"reviews":0,"subject":"math.PR","summary":"Can a Gaussian on a noninteger-dimensional fractal give a probabilistic realization of Edelman's ghosts and shadows? We distinguish a Gaussian-weighted Hausdorff measure, a radial Gaussian law, and a Gaussian random vector or field. For every real $\\beta>1$, we construct a closed cone of Hausdorff dimension $\\beta$ whose Gaussian-weighted $\\beta$-dimensional Hausdorff measure has exactly the $\\chi_\\beta$ radial distribution. The construction relies on exact radial volume growth, not merely on a dimension calculation. We prove a metric obstruction below dimension one and explain why the cone…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}