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- Title
Joint distribution of the cokernels of random p-adic matrices.
- Authors
Lee, Jungin
- Abstract
In this paper, we study the joint distribution of the cokernels of random p-adic matrices. Let p be a prime and let P 1 (t) , ... , P l (t) ∈ ℤ p [ t ] be monic polynomials whose reductions modulo p in 픽 p [ t ] are distinct and irreducible. We determine the limit of the joint distribution of the cokernels cok (P 1 (A)) , ... , cok (P l (A)) for a random n × n matrix A over ℤ p with respect to the Haar measure as n → ∞ . By applying the linearization of a random matrix model, we also provide a conjecture which generalizes this result. Finally, we provide a sufficient condition that the cokernels cok (A) and cok (A + B n) become independent as n → ∞ , where B n is a fixed n × n matrix over ℤ p for each n and A is a random n × n matrix over ℤ p .
- Subjects
RANDOM matrices; HAAR integral; POLYNOMIALS
- Publication
Forum Mathematicum, 2023, Vol 35, Issue 4, p1005
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2022-0209