Universality of the cokernels of random p-adic matrices with inhomogeneously balanced columns

@misc{lee2026universality,
  title = {{Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns}},
  author = {Jungin Lee and Sungjin Park},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.02180},
  eprint = {2606.02180},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02180},
}

TY  - UNPB
TI  - Universality of the cokernels of random p-adic matrices with inhomogeneously balanced columns
AU  - Jungin Lee
AU  - Sungjin Park
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2606.02180
UR  - https://arxiv.org/abs/2606.02180
AB  - In this paper, we prove universality of the distribution of the cokernels of random p-adic matrices with inhomogeneously balanced columns. More precisely, let u ≥ 0 be an integer, and for each positive integer n, let A(n) be a random n × (n+u) matrix over ℤ_p whose i-th column is α_n(i)-balanced. We prove that if ∑_i=1^n+u exp(−εα_n(i)n) → 0 as n → ∞ for every ε>0, then the cokernels of A(n) converge in distribution, as n → ∞, to the same limiting law as the cokernels of Haar-random n × (n+u) matrices over ℤ_p. This extends a universality theorem of Nguyen and Wood to random p-adic matrices with inhomogeneously balanced columns.
ER  -