Science AI Journal
Mathematics · Research topic

Open research questions in Random Matrices and Applications

99 unresolved questions extracted from the limitations and future-work sections of 591 Random Matrices and Applications papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • The paper identifies a gap in the literature regarding the geometric description of sampling sequences in one-sided and two-sided small Fock spaces. The paper notes that the problem of describing sampling sequences in Fock spaces is important and has been studied extensively.

    Shift-invariant sampling in two-sided small Fock spaces · 2026 · DOI

  • To investigate the incremental universality in other important ensembles, like sparse matrices, band matrices with wide band, block matrices, complex hermitean matrices.

    Incremental universality of Wigner random matrices · 2026 · DOI

  • The universality of Wigner random matrices has not been fully understood. The comparison of connected correlators of distinct ensembles has not been fully explored.

    Incremental universality of Wigner random matrices · 2026 · DOI

  • To study the fluctuations of the mod p rank of other types of random matrices. To develop new methods for studying the fluctuations of the mod p rank of triangular matrices.

    The fluctuations of the mod p rank of triangular matrices · 2026 · DOI

  • The existing literature on infinitely divisible modified Bessel distributions is limited. There is a need for new results on the properties of certain distributions.

    Infinitely divisible modified Bessel distributions · 2026 · DOI

  • A new proof of the result that the spectral distributions of the free positive multiplicative Brownian motion form a semigroup with respect to free multiplicative convolution is needed. The properties of the free positive multiplicative Brownian motion and its relation to the free additive convolution of semicircle and uniform distributions need to be further studied.

    Free Positive Multiplicative Brownian Motion and the Free Additive Convolution of Semicircle and Uniform Distributions · 2026 · DOI

  • The paper does not provide a comprehensive review of all existing literature on extreme value theory. The study focuses on subordinated Gaussian processes and does not address other types of processes. The paper assumes that the latent process can be represented as a multivariate causal linear process.

    On extremes for Gaussian subordination · 2026 · DOI

  • Future research can build on the paper's results to develop new statistical methods for analyzing extreme values. The study's findings can be used to inform the development of new models for predicting extreme events. The paper's introduction of m-extremal dependence can be explored further in future research.

    On extremes for Gaussian subordination · 2026 · DOI

  • The paper notes that the spectral framework established is general and holds for arbitrary 0-1 matrices. However, the paper also identifies the need for additional structural hypotheses to prevent low-frequency elements from accumulating large local supports.

    Spectral Properties and Localization Barriers of Co-occurrence Gram Matrices in Set Families · 2026 · DOI

  • The paper suggests that future research should address two specific structural alignment problems to leverage the spectral framework toward a complete resolution of Frankl's conjecture. The paper notes that additional research is needed to develop new algorithms and data structures for set systems.

    Spectral Properties and Localization Barriers of Co-occurrence Gram Matrices in Set Families · 2026 · DOI

  • The paper suggests that future research should focus on the development of new methods for constructing quasi-uniform point sets. The paper recommends that future research should investigate the quasi-uniformity properties of other types of quasi-Monte Carlo point sets. The paper proposes that future research should study the computational complexity of the constructions presented.

    On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences–Part I: Lattices and Kronecker sequences · 2026 · DOI

  • The paper identifies a gap in the understanding of the quasi-uniformity properties of quasi-Monte Carlo point sets. The paper notes that prior work has focused on the uniform distribution modulo 1 of (nα)-sequences, but has not studied their quasi-uniformity. The paper highlights the need for a comprehensive study of the quasi-uniformity properties of all types of quasi-Monte Carlo point sets.

    On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences–Part I: Lattices and Kronecker sequences · 2026 · DOI

  • To say something more precise about the distributions of certain parameters after appropriate centering and rescaling. To study the typical behavior of other numerical semigroup invariants. To study analogous problems for random generalized numerical semigroups.

    Statistics of Erdős–Rényi random numerical semigroups · 2026 · DOI

  • The orders of magnitude of certain parameters of Erdős–Rényi random numerical semigroups were not known. The behavior of random numerical semigroups was not well understood.

    Statistics of Erdős–Rényi random numerical semigroups · 2026 · DOI

  • The method remains well defined but universal consistency is no longer guaranteed if the generating kernel is not universal or cannot be well approximated by a universal kernel. The choice of embedding dimension d is crucial because the spectral decomposition of the adjacency matrix is used to approximate the feature map of the kernel.

    RKHS-Based Latent Position Random Graph Correlation · 2026 · DOI

  • To apply the proposed method to more complex network data. To develop more efficient algorithms for computing the proposed correlation coefficient. To study the theoretical properties of the proposed method in more detail.

    RKHS-Based Latent Position Random Graph Correlation · 2026 · DOI

  • The paper does not provide a detailed analysis of the computational complexity of the estimator. The paper assumes that the underlying drift function b is unknown.

    Nonparametric estimation of the jump rate in mean field interacting systems of neurons · 2026 · DOI

  • The paper identifies the need for a nonparametric estimator of the spiking rate function. The paper notes that the mean field limit provides a mesoscopic description of any single neuron by a theoretical limit dynamic.

    Nonparametric estimation of the jump rate in mean field interacting systems of neurons · 2026 · DOI

  • Further study of the properties of union-closed set families using the introduced framework. Application of the framework to other problems in combinatorics.

    Spectral Duality, Downward Shadow Coupling, and Localization Barriers in Union-Closed Set Families · 2026 · DOI

  • The lack of a unified framework for analyzing union-closed set families. The need for a novel approach to prove the unconditional lower bound for the frequency of elements in union-closed set families.

    Spectral Duality, Downward Shadow Coupling, and Localization Barriers in Union-Closed Set Families · 2026 · DOI

  • The law of the limiting fluctuations of the mod p rank of triangular matrices is not well understood. There is a need for a new method to study the fluctuations of the mod p rank of triangular matrices.

    The fluctuations of the mod p rank of triangular matrices · 2026 · DOI

  • In this paper, we show that for online / streaming algorithms the story is very different, and constant aspect ratio is insufficient for nonzero overlap.

    The Phase Transition in Online PCA Depends on $n/d\log(d)$, not $n/d$ · 2026

  • While this rate is known to be minimax optimal on $\mathbb R^d$ under strict assumptions with bounded kernels, little is known about its optimality beyond the finite-dimensional Euclidean setting with unbounded kernels.

    Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD · 2026

  • Writing $S(r,\varepsilon)$ for the sample complexity at additive error $\varepsilon$, we resolve the open problem posed by Wang by closing, up to logarithmic factors, the gap between the previously known bounds $Ω(r/\varepsilon^2)$ and $O(r^2/\varepsilon^2)$.

    The Sample Complexity of Fidelity Estimation to a Known Rank-$r$ Reference State Is $\widetildeΘ(r^2/\varepsilon^2)$ · 2026

  • To analyze the model with memory in more detail. To consider the case where the weights of opinions and interactions between persons are not constant.

    Iterative behaviour of generalized majority functions · 1983 · DOI

Most-cited papers in Random Matrices and Applications

Most recent work

Find a gap in your own Random Matrices and Applications sub-topic

This page shows what the Random Matrices and Applications literature already flags as unresolved. To narrow it to your specific question, run the guided finder — it searches the gap library on demand and checks candidates against 250M+ OpenAlex works.

Open the Research Gap Finder →

Related topics in Mathematics

Cognitive and developmental aspects of mathematical skills
398 open questions
Mathematics Education and Pedagogy
319 open questions
Statistics Education and Methodologies
146 open questions
Geometric Analysis and Curvature Flows
143 open questions
COVID-19 epidemiological studies
142 open questions
Advanced Causal Inference Techniques
140 open questions
Analytic Number Theory Research
118 open questions
Numerical methods for differential equations
113 open questions
99 open questions have been extracted from the limitations and future-work passages of 591 Random Matrices and Applications papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

Tools for your next paper

Gaps & Literature SearchFind open questions in any field — 120,000+ open gaps mined from our own library.Pre-CheckIs your paper ready? A Tier 1–5 acceptance probability in seconds.Journal FinderA ranked shortlist of target journals from a 17,500-venue index.Duplicate Publication CheckerCheck prior-publication & salami-slicing risk across 8 sources.Citation GeneratorFreeA DOI or title → APA, MLA, Vancouver, Chicago, BibTeX, RIS. No signup.Graphical Abstract MakerFreeTurn your findings into a colorblind-safe graphical abstract.

Compare the category — Honest roundups of the AI research tools, ours listed alongside the alternatives.

Command palette

Jump anywhere, run any action.