{"paper":{"title":"Determination of Boolean models by mean values of mixed volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Daniel Hug, Wolfgang Weil","submitted_at":"2017-12-21T22:55:07Z","abstract_excerpt":"In Weil (2001) formulas were proved for stationary Boolean models $Z$ in $\\mathbb{R}^d$ with convex or polyconvex grains, which express the densities of mixed volumes of $Z$ in terms of related mean values of the underlying Poisson particle process $X$. These formulas were then used to show that in dimensions 2 and 3 the mean values of $Z$ determine the intensity $\\gamma$ of $X$. For $d=4$ a corresponding result was also stated, but the proof given was incomplete, since in the formula for the mean Euler characteristic $\\overline V_0 (Z)$ a term $\\overline V^{(0)}_{2,2}(X,X)$ was missing. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08241","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"}