{"paper":{"title":"Transporting random measures on the line and embedding excursions into Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"unter Last, Hermann Thorisson, Wenpin Tang","submitted_at":"2016-08-05T20:31:54Z","abstract_excerpt":"We consider two jointly stationary and ergodic random measures $\\xi$ and $\\eta$ on the real line $\\mathbb{R}$ with equal intensities. An allocation is an equivariant random mapping from $\\mathbb{R}$ to $\\mathbb{R}$. We give sufficient and partially necessary conditions for the existence of allocations transporting $\\xi$ to $\\eta$. An important ingredient of our approach is to introduce a transport kernel balancing $\\xi$ and $\\eta$, provided these random measures are mutually singular. In the second part of the paper, we apply this result to the path decomposition of a two-sided Brownian motion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02016","kind":"arxiv","version":3},"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"}