About

Hoi Nguyen is a Professor in the Department of Mathematics at The Ohio State University. He earned his PhD from Rutgers University in 2010. His areas of expertise include combinatorics, probability, and stochastic processes. Nguyen's research focuses on these fields, contributing to the understanding of complex mathematical structures and probabilistic models. He is involved in academic activities within the department and collaborates on various research projects related to his areas of specialization.

Research topics

• Discrete mathematics
• Mathematical analysis
• Combinatorics
• Physics
• Mathematics

Selected publications

• Subcritical epidemics on random graphs

  Advances in Mathematics · 2025-01-07

  article1st authorCorresponding
  PublisherDOI

• Real Roots of Random Weyl Polynomials with General Coefficients: Expectation and Variance

  ArXiv.org · 2025-11-11

  preprintOpen access

  In this paper, we investigate the number of real zeros of random Weyl polynomials of degree \(n \to \infty\) with general coefficient distributions. Motivated by the results of arXiv:1409.4128 and arXiv:1402.4628 as well as arXiv:1711.03316 and arXiv:1912.11901, we determine how the expected number of real zeros and their variance, over various natural intervals, depend on the moments of the common coefficient distribution. Our main finding is that while the first-order asymptotic of the expectation is universal, the next-order correction depends on the third and fourth moments of the distribution, and may grow linearly with \(\log n\), depending on the interval under consideration. In contrast, for the variance we show that the leading-order term is universal, which differs from the behavior observed for random trigonometric polynomials in arXiv:1711.03316 and arXiv:1912.11901. Our approach relies on an Edgeworth expansion for random walks arising from Weyl polynomials, a result of independent interest.

  PublisherOA PDFDOI

• Combined posterior and left-sided superior mesenteric artery-first approach to the TRIANGLE operation for pancreatic cancer

  Annals of Hepato-Biliary-Pancreatic Surgery · 2025-07-14

  articleOpen access

  < 0.001). Additionally, the rate of tumor-positive resection margins, R1 (direct), was decreased. The duration of the operation was significantly longer, and blood loss was higher with the dual approach. There was no significant difference in postoperative mortality and complications between the two approaches. Utilizing the combined posterior and left-sided first approach to SMA in PD or TP with the TRIANGLE operation proved safe and effective for achieving R0 resection with favorable short-term outcomes in borderline resectable and locally advanced pancreatic cancer.

  PublisherOA PDFDOI

• Optimality conditions for global minimizers to a class of convex set optimization problem subjected to geometric constraints

  RAIRO. Operations research · 2025-02-26

  articleOpen accessSenior author

  In this paper, we study optimality conditions for both global and approximate minimizers to convex set optimization problems with geometric constraints. We first consider a form of Gerstewitz’s nonlinear scalarization function concerning the set-less relation introduced by Kuroiwa. Then, it is employed to construct a type of directional derivative and sub-gradient for cone-convex set-valued maps. We also give some properties and usual calculus rules for these concepts. Later, some necessary and sufficient conditions for global and approximate solutions are established. Examples are provided for analyzing and illustrating the obtained results.

  PublisherOA PDFDOI

• On the First Non-Universal Term in Random Polynomial Real Zeros

  ArXiv.org · 2025-09-15

  preprintOpen accessSenior author

  Let $P_n(x) = \sum_{k=0}^{n} ξ_k x^k$ be a Kac random polynomial, where the coefficients $ξ_k$ are i.i.d.\ copies of a given random variable $ξ$. Based on numerical experiments, it has been conjectured that if $ξ$ has mean zero, unit variance, and a finite $(2+\varepsilon_0)$-moment for some $\varepsilon_0&gt;0$, then \[ \mathbb{E}[N_{\mathbb{R}}(P_n)] \;=\; \frac{2}π \log n + C_ξ + o_n(1), \] where $N_{\mathbb{R}}(P_n)$ denotes the number of real roots of $P_n$, and $C_ξ$ is an absolute constant depending only on $ξ$, which is nonuniversal. Prior to this work, the existence of $C_ξ$ had only been established by Do-Nguyen-Vu (2015, \emph{Proc.\ Lond.\ Math.\ Soc.}) under the additional assumption that $ξ$ either admits a $(1+p)$-integrable density or is uniformly distributed on $\{\pm 1, \pm 2, \dots, \pm N\}$. In this paper, using a different method, we remove these extra conditions on $ξ$, and extend the result to the setting where the $ξ_k$ are independent but not necessarily identically distributed. Moreover, this proof strategy provides an alternative description of the constant $C_ξ$, and this new perspective serves as the key ingredient in establishing that $C_ξ$ depends continuously on the distribution of $ξ$.

  PublisherOA PDFDOI

• Concentration of the number of real roots of random polynomials

  Electronic Journal of Probability · 2025-01-01

  articleOpen access

  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. Our method is elementary and works well for many models of random polynomials, with Gaussian or non-Gaussian coefficients.

  PublisherOA PDFDOI

• Outcomes of radical intented surgery for hilar cholangiocarcinoma in Bach Mai Hospital

  Ministry of Science and Technology Vietnam · 2025-01-07

  articleOpen access
  PublisherDOI

• Eigenvalue gaps of the Laplacian of random graphs

  arXiv (Cornell University) · 2024-12-31

  preprintOpen access

  We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization, no-structure delocalization, overcrowding and small entries of the eigenvectors for the Laplacian model. These findings are of independent interest.

  PublisherOA PDFDOI

• Central Limit Theorem for the number of real roots of random orthogonal polynomials

  Annales de l Institut Henri Poincaré Probabilités et Statistiques · 2024-07-31

  preprint

  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 correlations are not necessarily the same.

  PublisherDOI

• Evaluation of the results of the modified Blumgartpancreatic-intestinal anastomosis technique according to Satoi in pancreaticoduodenectomy at Bach Mai Hospital

  Ministry of Science and Technology Vietnam · 2024-02-25

  articleOpen access

  Objectives: This study aims to research on the safety and effectiveness of the modified Blumgart pancreaticojejunostomy anastomosis by Satoi in Bach Mai Hospital. Research subjects: Seventy-three patients underwent modified Blumgart pancreaticojejunostomy anastomosis by Satoi after pancreaticoduodenectomy at Gastrointestinal and Hepato-Biliary-Pancreatic Surgery Department, Bach Mai Hospital between October 2020 and April 2023. Method: Cross-sectional study combining retrospective and prospective studies. The Blumgart anastomosis was modified to simplify with 2 U-shaped sutures. Results: The average age of the study subjects was 58.49±12.69 years; the age group over 60 accounted for over 50%; male/female ratio was ~1. The number of patients with complications was 22/73; the total number of complications was 33, including 3 grade-III-or-above complications, according to Clavien-Dindo: 1 case had complications of grade C pancreatic fistula causing late hemorrhage, from the common hepatic artery wall, needs re-surgery, 1 case needs hemostasis under intervention radiology, 1 case needs to be drained under ultrasound guidance, and no patient deaths. Conclusion: The modified Blumgart pancreaticojejunostomy by Satoi is a safe and effective technique.

  PublisherOA PDFDOI

Recent grants

• Singularity, Universality, and Smoothness of Random Walks

  NSF · $137k · 2016–2019

• CAREER: Littlewood-Offord Theory and Universality in Random Structures

  NSF · $400k · 2018–2024

• Inverse Problems and Their Applications

  NSF · $82k · 2013–2016

Frequent coauthors

• Van Vu

  47 shared

• Thanh Khiem Nguyen

  Bạch Mai Hospital

  32 shared

• Tuan Hiep Luong

  29 shared

• Yen Do

  University of Virginia

  18 shared

• Kim Khue Dang

  VinUniversity

  18 shared

• Van H. Vu

  16 shared

• Van Duy Le

  16 shared

• Hong Son Trinh

  Viet Duc Hospital

  14 shared

Labs

• Hoi Nguyen LabPI

Education

• Ph.D, Mathematics

  Rutgers, The State University of New Jersey

  2010

Awards & honors

• Graduate Teaching Awards