{"paper":{"title":"Equilibrium diffusion on the cone of discrete Radon measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diana Conache, Eugene Lytvynov, Yuri G. Kondratiev","submitted_at":"2015-03-13T17:51:20Z","abstract_excerpt":"Let $\\mathbb K(\\mathbb R^d)$ denote the cone of discrete Radon measures on $\\mathbb R^d$. There is a natural differentiation on $\\mathbb K(\\mathbb R^d)$: for a differentiable function $F:\\mathbb K(\\mathbb R^d)\\to\\mathbb R$, one defines its gradient $\\nabla^{\\mathbb K} F $ as a vector field which assigns to each $\\eta\\in \\mathbb K(\\mathbb R^d)$ an element of a tangent space $T_\\eta(\\mathbb K(\\mathbb R^d))$ to $\\mathbb K(\\mathbb R^d)$ at point $\\eta$. Let $\\phi:\\mathbb R^d\\times\\mathbb R^d\\to\\mathbb R$ be a potential of pair interaction, and let $\\mu$ be a corresponding Gibbs perturbation of (th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04166","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"}