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pro vyhledávání: '"Nguyen, Hoi"'
Autor:
Nguyen, Hoi H., Van Peski, Roger
We consider the cokernel $G_n = \mathbf{Cok}(A_{k} \cdots A_2 A_1)$ of a product of independent $n \times n$ random integer matrices with iid entries from generic nondegenerate distributions, in the regime where both $n$ and $k$ are sent to $\infty$
Externí odkaz:
http://arxiv.org/abs/2409.03099
Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some extent. O
Externí odkaz:
http://arxiv.org/abs/2402.08773
Autor:
Nguyen, Hoi H., Nguyen, Oanh
The Kac polynomial $$f_n(x) = \sum_{i=0}^{n} \xi_i x^i$$ with independent coefficients of variance 1 is one of the most studied models of random polynomials. It is well-known that the empirical measure of the roots converges to the uniform measure on
Externí odkaz:
http://arxiv.org/abs/2308.11515
Autor:
Nguyen, Hoi H., Pan, Amanda
In this note we show that the singular probability of the adjacency matrix of a random $d$-regular graph on $n$ vertices, where $d$ is fixed and $n \to \infty$, is bounded by $n^{-1/3+o(1)}$. This improves a recent bound by Huang. Our method is based
Externí odkaz:
http://arxiv.org/abs/2308.06461
We consider random orthonormal polynomials $$ P_{n}(x)=\sum_{i=0}^{n}\xi_{i}p_{i}(x), $$ where $\xi_{0}$, . . . , $\xi_{n}$ are independent random variables with zero mean, unit variance and uniformly bounded $(2+\ep_0)$-moments, and $\{p_n\}_{n=0}^{
Externí odkaz:
http://arxiv.org/abs/2212.14544
Autor:
Nguyen, Hoi H., Wood, Melanie Matchett
In this paper we study the cokernels of various random integral matrix models, including random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a systematic method to establish universality under very general randomness as
Externí odkaz:
http://arxiv.org/abs/2210.08526
Autor:
Nguyen, Hoi H., Van Peski, Roger
For random integer matrices $M_1,\ldots,M_k \in \operatorname{Mat}_n(\mathbb{Z})$ with independent entries, we study the distribution of the cokernel $\operatorname{cok}(M_1 \cdots M_k)$ of their product. We show that this distribution converges to a
Externí odkaz:
http://arxiv.org/abs/2209.14957
Autor:
Nguyen, Hoi H., Pan, Amanda
Publikováno v:
In European Journal of Combinatorics December 2024 122
In this note we study the number of real roots of a wide class of random orthogonal polynomials with gaussian coefficients. Using the method of Wiener Chaos we show that the fluctuation in the bulk is asymptotically gaussian, even when the local corr
Externí odkaz:
http://arxiv.org/abs/2111.09015
Autor:
Nguyen, Hoi H., Nguyen, Oanh
Publikováno v:
In Stochastic Processes and their Applications September 2024 175