Empirical Spectral Distribution for Product of Spherical Ensembles Article Swipe
Consider the product of $m$ independent $n\times n$ spherical ensembles for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. A recent paper by Zeng (2016) obtains the limit of the empirical spectral distribution for the product ensemble when $m$ is a fixed integer. In this paper, we investigate the limiting empirical spectral distribution for the product of spherical ensembles in the case when $m$ changes with $n$, that is, $m=m_n$ is an arbitrary sequence of positive integers.
Related Topics
Concepts
Spectral power distribution
Empirical distribution function
Distribution (mathematics)
Mathematics
Product (mathematics)
Limiting
Limit (mathematics)
Eigenvalues and eigenvectors
Sequence (biology)
Combinatorics
Statistical physics
Mathematical analysis
Physics
Statistics
Chemistry
Geometry
Quantum mechanics
Mechanical engineering
Biochemistry
Engineering
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1701.06926
- OA Status
- green
- References
- 15
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2582679725
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2582679725Canonical identifier for this work in OpenAlex
- Title
-
Empirical Spectral Distribution for Product of Spherical EnsemblesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
-
2017-01-24Full publication date if available
- Authors
-
Shuhua Chang, Yongcheng QiList of authors in order
- Landing page
-
https://arxiv.org/pdf/1701.06926Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1701.06926Direct OA link when available
- Concepts
-
Spectral power distribution, Empirical distribution function, Distribution (mathematics), Mathematics, Product (mathematics), Limiting, Limit (mathematics), Eigenvalues and eigenvectors, Sequence (biology), Combinatorics, Statistical physics, Mathematical analysis, Physics, Statistics, Chemistry, Geometry, Quantum mechanics, Mechanical engineering, Biochemistry, EngineeringTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
15Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2582679725 |
|---|---|
| doi | |
| ids.mag | 2582679725 |
| ids.openalex | https://openalex.org/W2582679725 |
| fwci | 0.0 |
| type | preprint |
| title | Empirical Spectral Distribution for Product of Spherical Ensembles |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11716 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2613 |
| topics[0].subfield.display_name | Statistics and Probability |
| topics[0].display_name | Random Matrices and Applications |
| topics[1].id | https://openalex.org/T11152 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9976000189781189 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2610 |
| topics[1].subfield.display_name | Mathematical Physics |
| topics[1].display_name | Stochastic processes and statistical mechanics |
| topics[2].id | https://openalex.org/T11901 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9958000183105469 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1702 |
| topics[2].subfield.display_name | Artificial Intelligence |
| topics[2].display_name | Bayesian Methods and Mixture Models |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C94360122 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7472556829452515 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1967557 |
| concepts[0].display_name | Spectral power distribution |
| concepts[1].id | https://openalex.org/C98385598 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6658514142036438 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q1339385 |
| concepts[1].display_name | Empirical distribution function |
| concepts[2].id | https://openalex.org/C110121322 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6360628604888916 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q865811 |
| concepts[2].display_name | Distribution (mathematics) |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.6234140396118164 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C90673727 |
| concepts[4].level | 2 |
| concepts[4].score | 0.599277675151825 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q901718 |
| concepts[4].display_name | Product (mathematics) |
| concepts[5].id | https://openalex.org/C188198153 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5522461533546448 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1613840 |
| concepts[5].display_name | Limiting |
| concepts[6].id | https://openalex.org/C151201525 |
| concepts[6].level | 2 |
| concepts[6].score | 0.5445795655250549 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q177239 |
| concepts[6].display_name | Limit (mathematics) |
| concepts[7].id | https://openalex.org/C158693339 |
| concepts[7].level | 2 |
| concepts[7].score | 0.49508562684059143 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q190524 |
| concepts[7].display_name | Eigenvalues and eigenvectors |
| concepts[8].id | https://openalex.org/C2778112365 |
| concepts[8].level | 2 |
| concepts[8].score | 0.41553401947021484 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q3511065 |
| concepts[8].display_name | Sequence (biology) |
| concepts[9].id | https://openalex.org/C114614502 |
| concepts[9].level | 1 |
| concepts[9].score | 0.3760078251361847 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[9].display_name | Combinatorics |
| concepts[10].id | https://openalex.org/C121864883 |
| concepts[10].level | 1 |
| concepts[10].score | 0.37194788455963135 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q677916 |
| concepts[10].display_name | Statistical physics |
| concepts[11].id | https://openalex.org/C134306372 |
| concepts[11].level | 1 |
| concepts[11].score | 0.2847142815589905 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[11].display_name | Mathematical analysis |
| concepts[12].id | https://openalex.org/C121332964 |
| concepts[12].level | 0 |
| concepts[12].score | 0.27188050746917725 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[12].display_name | Physics |
| concepts[13].id | https://openalex.org/C105795698 |
| concepts[13].level | 1 |
| concepts[13].score | 0.21634036302566528 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[13].display_name | Statistics |
| concepts[14].id | https://openalex.org/C185592680 |
| concepts[14].level | 0 |
| concepts[14].score | 0.09555959701538086 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q2329 |
| concepts[14].display_name | Chemistry |
| concepts[15].id | https://openalex.org/C2524010 |
| concepts[15].level | 1 |
| concepts[15].score | 0.09504184126853943 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[15].display_name | Geometry |
| concepts[16].id | https://openalex.org/C62520636 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0904456377029419 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[16].display_name | Quantum mechanics |
| concepts[17].id | https://openalex.org/C78519656 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q101333 |
| concepts[17].display_name | Mechanical engineering |
| concepts[18].id | https://openalex.org/C55493867 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q7094 |
| concepts[18].display_name | Biochemistry |
| concepts[19].id | https://openalex.org/C127413603 |
| concepts[19].level | 0 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[19].display_name | Engineering |
| keywords[0].id | https://openalex.org/keywords/spectral-power-distribution |
| keywords[0].score | 0.7472556829452515 |
| keywords[0].display_name | Spectral power distribution |
| keywords[1].id | https://openalex.org/keywords/empirical-distribution-function |
| keywords[1].score | 0.6658514142036438 |
| keywords[1].display_name | Empirical distribution function |
| keywords[2].id | https://openalex.org/keywords/distribution |
| keywords[2].score | 0.6360628604888916 |
| keywords[2].display_name | Distribution (mathematics) |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.6234140396118164 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/product |
| keywords[4].score | 0.599277675151825 |
| keywords[4].display_name | Product (mathematics) |
| keywords[5].id | https://openalex.org/keywords/limiting |
| keywords[5].score | 0.5522461533546448 |
| keywords[5].display_name | Limiting |
| keywords[6].id | https://openalex.org/keywords/limit |
| keywords[6].score | 0.5445795655250549 |
| keywords[6].display_name | Limit (mathematics) |
| keywords[7].id | https://openalex.org/keywords/eigenvalues-and-eigenvectors |
| keywords[7].score | 0.49508562684059143 |
| keywords[7].display_name | Eigenvalues and eigenvectors |
| keywords[8].id | https://openalex.org/keywords/sequence |
| keywords[8].score | 0.41553401947021484 |
| keywords[8].display_name | Sequence (biology) |
| keywords[9].id | https://openalex.org/keywords/combinatorics |
| keywords[9].score | 0.3760078251361847 |
| keywords[9].display_name | Combinatorics |
| keywords[10].id | https://openalex.org/keywords/statistical-physics |
| keywords[10].score | 0.37194788455963135 |
| keywords[10].display_name | Statistical physics |
| keywords[11].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[11].score | 0.2847142815589905 |
| keywords[11].display_name | Mathematical analysis |
| keywords[12].id | https://openalex.org/keywords/physics |
| keywords[12].score | 0.27188050746917725 |
| keywords[12].display_name | Physics |
| keywords[13].id | https://openalex.org/keywords/statistics |
| keywords[13].score | 0.21634036302566528 |
| keywords[13].display_name | Statistics |
| keywords[14].id | https://openalex.org/keywords/chemistry |
| keywords[14].score | 0.09555959701538086 |
| keywords[14].display_name | Chemistry |
| keywords[15].id | https://openalex.org/keywords/geometry |
| keywords[15].score | 0.09504184126853943 |
| keywords[15].display_name | Geometry |
| keywords[16].id | https://openalex.org/keywords/quantum-mechanics |
| keywords[16].score | 0.0904456377029419 |
| keywords[16].display_name | Quantum mechanics |
| language | en |
| locations[0].id | mag:2582679725 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | arXiv (Cornell University) |
| locations[0].landing_page_url | https://arxiv.org/pdf/1701.06926 |
| authorships[0].author.id | https://openalex.org/A5108100224 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Shuhua Chang |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Shuhua Chang |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5019013453 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-0761-9522 |
| authorships[1].author.display_name | Yongcheng Qi |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Yongcheng Qi |
| authorships[1].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/1701.06926 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Empirical Spectral Distribution for Product of Spherical Ensembles |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-10-10T17:16:08.811792 |
| primary_topic.id | https://openalex.org/T11716 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2613 |
| primary_topic.subfield.display_name | Statistics and Probability |
| primary_topic.display_name | Random Matrices and Applications |
| related_works | https://openalex.org/W2951766648, https://openalex.org/W2594726244, https://openalex.org/W1604331816, https://openalex.org/W1886221433, https://openalex.org/W2972987528, https://openalex.org/W2943834713, https://openalex.org/W1160897469, https://openalex.org/W2020050813, https://openalex.org/W2416792165, https://openalex.org/W1968487819, https://openalex.org/W2964227660, https://openalex.org/W2950564208, https://openalex.org/W2900777159, https://openalex.org/W3127289814, https://openalex.org/W2899194564, https://openalex.org/W2475012445, https://openalex.org/W2948108849, https://openalex.org/W2965465119, https://openalex.org/W3104337300, https://openalex.org/W2564075690 |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | mag:2582679725 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | arXiv (Cornell University) |
| best_oa_location.landing_page_url | https://arxiv.org/pdf/1701.06926 |
| primary_location.id | mag:2582679725 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | arXiv (Cornell University) |
| primary_location.landing_page_url | https://arxiv.org/pdf/1701.06926 |
| publication_date | 2017-01-24 |
| publication_year | 2017 |
| referenced_works | https://openalex.org/W1520752838, https://openalex.org/W1965415666, https://openalex.org/W1813708725, https://openalex.org/W1978864992, https://openalex.org/W3105472625, https://openalex.org/W2963434281, https://openalex.org/W3101063317, https://openalex.org/W1886221433, https://openalex.org/W2092583264, https://openalex.org/W1675320962, https://openalex.org/W2950530649, https://openalex.org/W615589970, https://openalex.org/W2058790423, https://openalex.org/W2085871147, https://openalex.org/W1964910031 |
| referenced_works_count | 15 |
| abstract_inverted_index.A | 30 |
| abstract_inverted_index.a | 51 |
| abstract_inverted_index.In | 54 |
| abstract_inverted_index.an | 82 |
| abstract_inverted_index.by | 33 |
| abstract_inverted_index.in | 70 |
| abstract_inverted_index.is | 24, 50, 81 |
| abstract_inverted_index.n$ | 7 |
| abstract_inverted_index.of | 3, 21, 39, 67, 85 |
| abstract_inverted_index.on | 17 |
| abstract_inverted_index.we | 57 |
| abstract_inverted_index.$m$ | 4, 49, 74 |
| abstract_inverted_index.$n$ | 19 |
| abstract_inverted_index.1$. | 12 |
| abstract_inverted_index.The | 13 |
| abstract_inverted_index.for | 10, 44, 64 |
| abstract_inverted_index.is, | 79 |
| abstract_inverted_index.the | 1, 18, 22, 26, 37, 40, 45, 59, 65, 71 |
| abstract_inverted_index.$n$, | 77 |
| abstract_inverted_index.Zeng | 34 |
| abstract_inverted_index.case | 72 |
| abstract_inverted_index.that | 78 |
| abstract_inverted_index.this | 55 |
| abstract_inverted_index.when | 48, 73 |
| abstract_inverted_index.with | 76 |
| abstract_inverted_index.$m\ge | 11 |
| abstract_inverted_index.based | 16 |
| abstract_inverted_index.fixed | 52 |
| abstract_inverted_index.limit | 38 |
| abstract_inverted_index.paper | 32 |
| abstract_inverted_index.(2016) | 35 |
| abstract_inverted_index.called | 25 |
| abstract_inverted_index.paper, | 56 |
| abstract_inverted_index.recent | 31 |
| abstract_inverted_index.$m=m_n$ | 80 |
| abstract_inverted_index.changes | 75 |
| abstract_inverted_index.obtains | 36 |
| abstract_inverted_index.product | 2, 23, 46, 66 |
| abstract_inverted_index.$n\times | 6 |
| abstract_inverted_index.Consider | 0 |
| abstract_inverted_index.ensemble | 47 |
| abstract_inverted_index.integer. | 53 |
| abstract_inverted_index.limiting | 60 |
| abstract_inverted_index.positive | 86 |
| abstract_inverted_index.sequence | 84 |
| abstract_inverted_index.spectral | 28, 42, 62 |
| abstract_inverted_index.arbitrary | 83 |
| abstract_inverted_index.empirical | 14, 27, 41, 61 |
| abstract_inverted_index.ensembles | 9, 69 |
| abstract_inverted_index.integers. | 87 |
| abstract_inverted_index.spherical | 8, 68 |
| abstract_inverted_index.eigenvalues | 20 |
| abstract_inverted_index.independent | 5 |
| abstract_inverted_index.investigate | 58 |
| abstract_inverted_index.distribution | 15, 43, 63 |
| abstract_inverted_index.distribution. | 29 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |