{"paper":{"title":"Geometry of Gaussian signals","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Alberto Rosso, Raoul Santachiara, Werner Krauth","submitted_at":"2005-03-06T16:32:03Z","abstract_excerpt":"We consider Gaussian signals, i.e. random functions $u(t)$ ($t/L \\in [0,1]$) with independent Gaussian Fourier modes of variance $\\sim 1/q^{\\alpha}$, and compute their statistical properties in small windows $[x, x+\\delta]$. We determine moments of the probability distribution of the mean square width of $u(t)$ in powers of the window size $\\delta$. We show that the moments, in the small-window limit $\\delta \\ll 1$, become universal, whereas they strongly depend on the boundary conditions of $u(t)$ for larger $\\delta$. For $\\alpha > 3$, the probability distribution is computed in the small-win"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0503134","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}