Local limits in p-adic random matrix theory

被引:0
作者
Van Peski, Roger [1 ]
机构
[1] KTH Royal Inst Technol, Lindstedtsvagen 25, S-10044 Stockholm, Sweden
基金
欧洲研究理事会;
关键词
SINGULAR-VALUES; PRODUCTS; EDGE; DISTRIBUTIONS; FLUCTUATIONS; POLYNOMIALS;
D O I
10.1112/plms.12626
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the distribution of singular numbers of products of certain classes of p-adic random matrices, as both the matrix size and number of products go to infinity simultaneously. In this limit, we prove convergence of the local statistics to a new random point configuration on Z, defined explicitly in terms of certain intricate mixed q-series/exponential sums. This object may be viewed as a nontrivial p-adic analogue of the interpolating distributions of Akemann-Burda-Kieburg, which generalize the sine and Airy kernels and govern limits of complex matrix products. Our proof uses new Macdonald process computations and holds for matrices with iid additive Haar entries, corners of Haar matrices from GL(N)(Z(p)), and the p-adic analogue of Dyson Brownian motion studied by the author (https://arxiv.org/pdf/2309.02865).
引用
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页数:91
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