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- Title
Joint distribution of the cokernels of random p-adic matrices II.
- Authors
Jung, Jiwan; Lee, Jungin
- Abstract
In this paper, we study the combinatorial relations between the cokernels cok (A n + p x i I n ) ( 1 ≤ i ≤ m ), where A n is an n × n matrix over the ring of p-adic integers ℤ p , I n is the n × n identity matrix and x 1 , ... , x m are elements of ℤ p whose reductions modulo p are distinct. For a positive integer m ≤ 4 and given x 1 , ... , x m ∈ ℤ p , we determine the set of m-tuples of finitely generated ℤ p -modules (H 1 , ... , H m) for which (cok (A n + p x 1 I n ) , ... , cok (A n + p x m I n )) = (H 1 , ... , H m) for some matrix A n . We also prove that if A n is an n × n Haar random matrix over ℤ p for each positive integer n, then the joint distribution of cok (A n + p x i I n ) ( 1 ≤ i ≤ m ) converges as n → ∞ .
- Subjects
MATRIX rings; RINGS of integers; RANDOM matrices; INTEGERS; P-adic analysis
- Publication
Forum Mathematicum, 2024, Vol 36, Issue 4, p1119
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2023-0131