{"paper":{"title":"Rigidity and tolerance for perturbed lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Sly, Yuval Peres","submitted_at":"2014-09-16T02:53:05Z","abstract_excerpt":"A perturbed lattice is a point process $\\Pi=\\{x+Y_x:x\\in \\mathbb{Z}^d\\}$ where the lattice points in $\\mathbb{Z}^d$ are perturbed by i.i.d.\\ random variables $\\{Y_x\\}_{x\\in \\mathbb{Z}^d}$. A random point process $\\Pi$ is said to be rigid if $|\\Pi\\cap B_0(1)|$, the number of points in a ball, can be exactly determined given $\\Pi \\setminus B_0(1)$, the points outside the ball. The process $\\Pi$ is called deletion tolerant if removing one point of $\\Pi$ yields a process with distribution indistinguishable from that of $\\Pi$. Suppose that $Y_x\\sim N_d(0,\\sigma^2 I)$ are Gaussian vectors with with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4490","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"}