[HTML][HTML] Universality for cokernels of random matrix products
HH Nguyen, R Van Peski - Advances in Mathematics, 2024 - Elsevier
For random integer matrices M 1,…, M k∈ Mat n (Z) with independent entries, we study the
distribution of the cokernel Cok (M 1⋯ M k) of their product. We show that this distribution …
distribution of the cokernel Cok (M 1⋯ M k) of their product. We show that this distribution …
Local limits in pp‐adic random matrix theory
R Van Peski - Proceedings of the London Mathematical …, 2024 - Wiley Online Library
We study the distribution of singular numbers of products of certain classes of pp‐adic
random matrices, as both the matrix size and number of products go to∞ ∞ simultaneously …
random matrices, as both the matrix size and number of products go to∞ ∞ simultaneously …
A phase transition for the cokernels of random band matrices over the p-adic integers
A Mészáros - arXiv preprint arXiv:2408.13037, 2024 - arxiv.org
arXiv:2408.13037v1 [math.PR] 23 Aug 2024 A phase transition for the cokernels of random
band matrices over the p-adic integers Page 1 arXiv:2408.13037v1 [math.PR] 23 Aug 2024 A …
band matrices over the p-adic integers Page 1 arXiv:2408.13037v1 [math.PR] 23 Aug 2024 A …
Cohen-Lenstra distribution for sparse matrices with determinantal biasing
A Mészáros - arXiv preprint arXiv:2307.04741, 2023 - arxiv.org
Let us consider the following matrix $ B_n $. The columns of $ B_n $ are indexed with
$[n]=\{1, 2,\dots, n\} $ and the rows are indexed with $[n]^ 3$. The row corresponding to …
$[n]=\{1, 2,\dots, n\} $ and the rows are indexed with $[n]^ 3$. The row corresponding to …
Joint distribution of the cokernels of random p-adic matrices
J Lee - Forum Mathematicum, 2023 - degruyter.com
In this paper, we study the joint distribution of the cokernels of random p-adic matrices. Let p
be a prime and let P 1(t),…, P l(t)∈ ℤ p[t] be monic polynomials whose reductions …
be a prime and let P 1(t),…, P l(t)∈ ℤ p[t] be monic polynomials whose reductions …
Reflecting Poisson walks and dynamical universality in -adic random matrix theory
R Van Peski - arXiv preprint arXiv:2312.11702, 2023 - arxiv.org
We prove dynamical local limits for the singular numbers of $ p $-adic random matrix
products at both the bulk and edge. The limit object which we construct, the reflecting …
products at both the bulk and edge. The limit object which we construct, the reflecting …
What is a -adic Dyson Brownian motion?
R Van Peski - arXiv preprint arXiv:2309.02865, 2023 - arxiv.org
We consider the singular numbers of a certain explicit continuous-time Markov jump process
on $\mathrm {GL} _N (\mathbb {Q} _p) $, which we argue gives the closest $ p $-adic …
on $\mathrm {GL} _N (\mathbb {Q} _p) $, which we argue gives the closest $ p $-adic …
Polynomial equations for matrices over integers modulo a prime power and the cokernel of a random matrix
G Cheong, Y Liang, M Strand - Linear Algebra and its Applications, 2023 - Elsevier
Given a prime p and a positive integer k, let M n (Z/pk Z) be the ring of n× n matrices over
Z/pk Z. We consider the number of solutions X∈ M n (Z/pk Z) to the polynomial equation P …
Z/pk Z. We consider the number of solutions X∈ M n (Z/pk Z) to the polynomial equation P …
Mixed moments and the joint distribution of random groups
J Lee - Journal of Algebra, 2024 - Elsevier
We study the joint distribution of random abelian and non-abelian groups. In the abelian
case, we prove several universality results for the joint distribution of the multiple cokernels …
case, we prove several universality results for the joint distribution of the multiple cokernels …
Symmetric functions and the explicit moment problem for abelian groups
R Van Peski - arXiv preprint arXiv:2402.16625, 2024 - arxiv.org
arXiv:2402.16625v1 [math.CO] 26 Feb 2024 Page 1 arXiv:2402.16625v1 [math.CO] 26 Feb
2024 SYMMETRIC FUNCTIONS AND THE EXPLICIT MOMENT PROBLEM FOR ABELIAN …
2024 SYMMETRIC FUNCTIONS AND THE EXPLICIT MOMENT PROBLEM FOR ABELIAN …