{"paper":{"title":"Trimming a Tree and the Two-Sided Skorohod Reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer","submitted_at":"2014-04-18T16:02:19Z","abstract_excerpt":"The $h$-trimming of a tree is a natural regularization procedure which consists in pruning the small branches of a tree: given $h\\geq0$, it is obtained by only keeping the vertices having at least one leaf above them at a distance greater or equal to $h$.\n  The $h$-cut of a function $f$ is the function of minimal total variation uniformly approximating the increments of $f$ with accuracy $h$, and can be explicitly constructed via the two-sided Skorohod reflection of $f$ on the interval $[0,h]$.\n  In this work, we show that the contour path of the $h$-trimming of a rooted real tree is given by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4829","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"}