Universality for cokernels of random matrix products.(English)Zbl 07801728
For \(M\in \mathrm{M}_n(\mathbb{Z})\), the cokernel \(\mathbf{Cok}(M)=\mathbb{Z}^n/M \mathbb{Z}^n\). In this paper under review, the authors show that for \(M_1, \ldots, M_k \in \operatorname{Mat}_n(\mathbb{Z})\), the distribution of \(\mathbf{Cok}( M_1 \cdots M_k)\) converges to a universal one as \( n\to \infty\) for a general class of matrix entry distributions. More generally, they also show universal limits for the joint distribution of \(\mathbf{Cok}(M_1), \mathbf{Cok}(M_1M_2), \ldots \mathbf{Cok}(M_1 \cdots M_k)\). These results are extensions of the existing single-matrix universality case in the work ofM. M. Wood [Am. J. Math. 141, No. 2, 383–398 (2019;Zbl 1446.11170)].
As a consequence, they obtain an explicit universal distribution for coranks of random matrix products over \(\mathbb{F}_p\) as the matrix size tends to infinity.
As a consequence, they obtain an explicit universal distribution for coranks of random matrix products over \(\mathbb{F}_p\) as the matrix size tends to infinity.
Reviewer: Sami Omar (Sukhair)
MSC:
| 11M50 | Relations with random matrices |
| 15B52 | Random matrices (algebraic aspects) |
| 05E05 | Symmetric functions and generalizations |
| 05C80 | Random graphs (graph-theoretic aspects) |
| 60B20 | Random matrices (probabilistic aspects) |
Cite
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