{"paper":{"title":"Limiting Spectral Distribution of Block Matrices with Toeplitz Block Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arup Bose, Rajat Subhra Hazra, Riddhipratim Basu, Shirshendu Ganguly","submitted_at":"2011-11-08T13:22:53Z","abstract_excerpt":"We study two specific symmetric random block Toeplitz (of dimension $k \\times k$) matrices: where the blocks (of size $n \\times n$) are (i) matrices with i.i.d. entries, and (ii) asymmetric Toeplitz matrices.\n  Under suitable assumptions on the entries, their limiting spectral distributions (LSDs) exist (after scaling by $\\sqrt{nk}$) when (a) $k$ is fixed and $n \\to\\infty$ (b) $n$ is fixed and $k\\rightarrow \\infty$ (c) $n$ and $k$ go to $\\infty$ simultaneously. Further the LSD's obtained in (a) and (b) coincide with those in (c) when $n$ or respectively $k$ tends to infinity. This limit in (c)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1901","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"}