4 research outputs found
Local limits in -adic random matrix theory
We study the distribution of singular numbers of products of certain classes
of -adic random matrices, as both the matrix size and number of products go
to simultaneously. In this limit, we prove convergence of the local
statistics to a new random point configuration on , defined
explicitly in terms of certain intricate mixed -series/exponential sums.
This object may be viewed as a nontrivial -adic analogue of the
interpolating distributions of Akemann-Burda-Kieburg arXiv:1809.05905, 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
, and the -adic analogue of Dyson Brownian
motion studied in arXiv:2112.03725.Comment: 71 pages, 9 figures. Comments welcome! v2: minor corrections to
asymptotic analysis in proofs of Theorem 4.1 and Proposition 9.1, and several
typos fixed and references adde