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Joint distribution of the cokernels of random p-adic matrices II

  • Jiwan Jung and Jungin Lee ORCID logo EMAIL logo
Published/Copyright: February 20, 2024

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 p , I n is the n × n identity matrix and x 1 , , x m are elements of p whose reductions modulo p are distinct. For a positive integer m 4 and given x 1 , , x m p , we determine the set of m-tuples of finitely generated 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 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 .

Keywords: moments
MSC 2020: 15B52; 60B20

Communicated by Freydoon Shahidi


Funding statement: Jiwan Jung was partially supported by Samsung Science and Technology Foundation (SSTF-BA2001-04). Jungin Lee was supported by the new faculty research fund of Ajou University (S-2023-G0001-00236).

Acknowledgements

The authors thank Gilyoung Cheong and Seongsu Jeon for their helpful comments.

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Received: 2023-04-10
Published Online: 2024-02-20
Published in Print: 2024-07-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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