{"paper":{"title":"Law of Large Numbers for Infinite Random Matrices over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA","math.RT"],"primary_cat":"math.PR","authors_text":"Alexey Bufetov, Leonid Petrov","submitted_at":"2014-02-07T21:18:14Z","abstract_excerpt":"Asymptotic representation theory of general linear groups GL(n,q) over a finite field leads to studying probability measures \\rho on the group U of all infinite uni-uppertriangular matrices over F_q, with the condition that \\rho is invariant under conjugations by arbitrary infinite matrices. Such probability measures form an infinite-dimensional simplex, and the description of its extreme points (in other words, ergodic measures \\rho) was conjectured by Kerov in connection with nonnegative specializations of Hall-Littlewood symmetric functions.\n  Vershik and Kerov also conjectured the followin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1772","kind":"arxiv","version":2},"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"}