August 23, 2024Open Access

A phase transition for the cokernels of random band matrices over the p-adic integers

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Abstract

Let Bₙ be an n× n Haar-uniform band matrix over Zₚ with band width wₙ. We prove that cok(Bₙ) has Cohen-Lenstra limiting distribution if and only if \[limn→∞ (w_n-log_p(n))=+∞.\]

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András Mészáros (2024) studied this question.

synapsesocial.com/papers/68e5b296b6db64358754c084 https://doi.org/10.48550/arxiv.2408.13037

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Abstract

Let Bₙ be an n× n Haar-uniform band matrix over Zₚ with band width wₙ. We prove that cok(Bₙ) has Cohen-Lenstra limiting distribution if and only if \[limn→∞ (w_n-log_p(n))=+∞.\]

A phase transition for the cokernels of random band matrices over the p-adic integers

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A phase transition for the cokernels of random band matrices over the p-adic integers

Abstract

Discussion

Cite This Study

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