Science Explorer Back to mapMap
Discussion
Topic · Statistics and Probability

Random Matrices and Applications

Random Matrices and Applications is a research topic within Statistics and Probability. Science Explorer counts 10k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers the topic of Random Matrix Theory and its applications in various fields such as eigenvalues, covariance matrices, universality, spectral statistics, large dimensional data, spiked population models, principal component analysis, determinantal processes, and growth processes.

  • Random Matrix Theory
  • Eigenvalues
  • Covariance Matrices
  • Universality
  • Spectral Statistics
  • Large Dimensional Data
  • Spiked Population Models
  • Principal Component Analysis
  • Determinantal Processes
  • Growth Processes
Research works
10k
fractional, since 1950
In the world top 10%
1.1k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+11%
the tick is no change
Largest producer
United States
29% of the 10 largest, 2022-now
Random Matrices and Applications

Which countries lead Random Matrices and Applications research?

By volume, the United States and China publish the most (392 and 283 works in 2022-now).

By volume, 2022-now

  1. 1 United States 392 works
  2. 2 China 283 works
  3. 3 France 178 works
  4. 4 Germany 100 works
  5. 5 Japan 88 works
  6. 6 United Kingdom 85 works
  7. 7 Russia 59 works
  8. 8 India 54 works
  9. 9 Italy 46 works
  10. 10 Canada 45 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 29.4%China: 21.3%France: 13.4%Germany: 7.5%6 others listed: 28.3%29%largest
United States392 · 29.4%China283 · 21.3%France178 · 13.4%Germany100 · 7.5%6 others listed377 · 28.3%

Shares of the rows listed above, not of the whole node.

Which institutions lead Random Matrices and Applications research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Random Matrices and Applications research, followed by Russian Academy of Sciences and New York University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 77 works
  2. 2 Russian Academy of SciencesRussia 25 works
  3. 3 New York UniversityUnited States 17 works
  4. 4 Columbia UniversityUnited States 16 works
  5. 5 Massachusetts Institute of TechnologyUnited States 16 works
  6. 6 University of California, BerkeleyUnited States 13 works
  7. 7 Stanford UniversityUnited States 13 works
  8. 8 Chinese Academy of SciencesChina 13 works
  9. 9 University of TorontoCanada 12 works
  10. 10 Anhui UniversityChina 11 works

Who are the leading researchers in Random Matrices and Applications?

The most-cited researchers publishing on Random Matrices and Applications include Robert John Tibshirani, Trevor Hastie and Yann LeCun.

  1. 1 Robert John Tibshirani United States 396k citations
  2. 2 Trevor Hastie United States 301k citations
  3. 3 Yann LeCun United States 256k citations
  4. 4 Harry Eugene Stanley United States 198k citations
  5. 5 Michael I. Jordan United States 182k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Random Matrices and Applications?

The most cited paper in Random Matrices and Applications is "Writing on dirty paper (Corresp.)" (Mónica Isabel Teixeira Costa, 1983), with 3,826 citations. Next come "Differential Privacy: A Survey of Results" (3,407) and "A well-conditioned estimator for large-dimensional covariance matrices" (3,093).

Most cited papers
#PaperReleasedCitations
1 Writing on dirty paper (Corresp.) Mónica Isabel Teixeira Costa · IEEE Transactions on Information Theory May 1983 3,826
2 Differential Privacy: A Survey of Results Cynthia Dwork · Lecture notes in computer science Conference paper 29 Apr 2008 3,407
3 A well-conditioned estimator for large-dimensional covariance matrices Olivier Ledoit, Michael Wolf · Journal of Multivariate Analysis Open access 16 Jul 2003 3,093
4 Quantum statistical mechanics in a closed system Joshua M. Deutsch · Physical Review A Feb 1991 2,959
5 For most large underdetermined systems of linear equations the minimal 𝓁 1 ‐norm solution is also the sparsest solution David L. Donoho · Communications on Pure and Applied Mathematics 23 Mar 2006 2,544
All 96 most cited papers, with filters and sorting

Where is Random Matrices and Applications research done?

The largest centres of Random Matrices and Applications research in 2022-now are Paris (France), Beijing (China), New York (United States) and Tokyo (Japan).

Largest cities, 2022-now

  1. 1 ParisFrance 68 works
  2. 2 BeijingChina 54 works
  3. 3 New YorkUnited States 36 works
  4. 4 TokyoJapan 33 works
  5. 5 MoscowRussia 32 works
  6. 6 ShanghaiChina 23 works
  7. 7 CambridgeUnited States 23 works
  8. 8 HefeiChina 22 works
  9. 9 LondonUnited Kingdom 19 works
  10. 10 SeoulSouth Korea 15 works
See Random Matrices and Applications on the map

Where is the best place to study Random Matrices and Applications?

Among universities, judged by research, Columbia University, Massachusetts Institute of Technology and University of California, Berkeley score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 19.81%fractional works in this field (log) →share of work in the world top 10% →Columbia UniversityUniversity of Califo…Massachusetts Instit…New York University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Columbia UniversityUnited States 72.019.8%9.4×16 +14.6%
2Massachusetts Institute of TechnologyUnited States 69.913.7%14.5×16 +31.1%
3University of California, BerkeleyUnited States 66.717.1%9.1×13 +40.0%
4New York UniversityUnited States 66.013.5%9.7×17 +6.8%
5Anhui UniversityChina 62.822.7%15.9×11 +31.5%
6Princeton UniversityUnited States 60.029.7%12.7×9 -3.2%
7Université Paris Sciences et LettresFrance 58.224.8%14.8×9 +4.9%
8ETH ZurichSwitzerland 56.029.4%7.7×8 +32.6%
9Institute of Science and Technology AustriaAustria 54.817.8%154.2×8 +80.8%
10Stanford UniversityUnited States 53.79.6%5.8×13 +17.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Random Matrices and Applications, country by country

Is Random Matrices and Applications research growing?

Output in 2022-2025 was 11% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Random Matrices and Applications.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Random Matrices and Applications as a percentage of every work published that year, 0.0062% in 2024.

still counting0.010%0.020%Random Matrices and Applications0.0068% in 202519801990200020102020

Fractional works of Random Matrices and Applications over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Random Matrices and Applications9.6% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

Discussion

Ask a question or share a note about Random Matrices and Applications. Posts are plain text and can be reported.