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arXiv · 2008.10732

On the distribution of equivalence classes of random symmetric p-adic matrices

Valeriya Kovaleva
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Abstract

We consider random symmetric matrices with independent entries distributed according to the Haar measure on $\mathbb{Z}_p$ for odd primes $p$ and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones, and Keating on the probability that a random quadratic form over $\mathbb{Z}_p$ has a non-trivial zero.

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Valeriya Kovaleva. 2020-08-24. On the distribution of equivalence classes of random symmetric p-adic matrices. https://doi.org/10.1112/mtk.12212

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