Universality of the Cokernels of Random p-adic Matrices with Inhomogeneously Balanced Columns
- 주제(키워드) random matrices , cokernels , Cohen–Lenstra heuristics , universality , padic matrices
- 주제(DDC) 510
- 발행기관 아주대학교 일반대학원
- 지도교수 이정인
- 발행년도 2026
- 학위수여년월 2026. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/ajou/000000036212
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
In this paper, we prove universality of the distribution of the cokernels of a random p-adic matrix with inhomogeneously balanced columns. More precisely, let u ≥ 0 be an integer and let {A_n} be a sequence of random n × （n + u） matrices over Zp whose i-th column is alpha_n（i）-balanced. We prove that if sum_{i=1}^{n+u} exp（−ϵαn（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 Zp. This extends a universality theorem of Nguyen and Wood to random p-adic matrices with inhomogeneously balanced columns. Keywords: random matrices, cokernels, Cohen–Lenstra heuristics, universality, p- adic matrices
more목차
1 Introduction 1
2 Preliminaries 5
2.1 Ideal class groups and the Cohen–Lenstra heuristics 5
2.2 Function field analogues and random matrix models 6
2.3 The moment method 7
3 Main Results 9
3.1 Proof of main theorem 11
3.2 An example 16
Bibliography 17
