{"paper":{"title":"Superposition of plane waves in high spatial dimensions: from landscape complexity to the deepest minimum value","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Bertrand Lacroix-A-Chez-Toine, Yan V. Fyodorov","submitted_at":"2024-11-14T18:54:04Z","abstract_excerpt":"In this article, we introduce and analyse some statistical properties of a class of models of random landscapes of the form ${\\cal H}({\\bf x})=\\frac{\\mu}{2}{\\bf x}^2+\\sum_{l=1}^M \\phi_l({\\bf k}_l\\cdot {\\bf x}), \\, \\, {\\bf x}\\in \\mathbb{R}^N,\\,\\, \\mu>0 $ where both the functions $\\phi_l(z)$ and vectors ${\\bf k}_l$ are random. An important example of such landscape describes superposition of $M$ plane waves with random amplitudes, directions of the wavevectors, and phases, further confined by a parabolic potential of curvature $\\mu$.\n  Our main efforts are directed towards analysing the landscap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09687","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09687/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}