{"paper":{"title":"Limiting spectral distribution of a new random matrix model with dependence across rows and columns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eckhard Schlemm, Oliver Pfaffel","submitted_at":"2012-01-19T18:27:15Z","abstract_excerpt":"We introduce a random matrix model where the entries are dependent across both rows and columns. More precisely, we investigate matrices of the form $\\X=(X_{(i-1)n+t})_{it}\\in\\R^{p\\times n}$ derived from a linear process $X_t=\\sum_j c_j Z_{t-j}$, where the $\\{Z_t\\}$ are independent random variables with bounded fourth moments. We show that, when both $p$ and $n$ tend to infinity such that the ratio $p/n$ converges to a finite positive limit $y$, the empirical spectral distribution of $p^{-1}\\X\\X^{\\T}$ converges almost surely to a deterministic measure. This limiting measure, which depends on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4134","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"}