A random matrix model for the Gaussian distribution View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2006-03

AUTHORS

Víctor Pérez-Abreu

ABSTRACT

The Gaussian unitary ensemble is a random matrix model (RMM) for the Wigner law. While random matrices in this model are infinitely divisible, the Wigner law is infinitely divisible not in the classical but in the free sense. We prove that any variance mixture of Gaussian distributions -- whether infinitely divisible or not in the classical sense -- admits a RMM of non Gaussian infinitely divisible random matrices. More generally, it is shown that any mixture of the Wigner law admits a RMM. A key role is played by the fact that the Gaussian distribution is the mixture of Wigner law with the ]]>2$-gamma distribution. More... »

PAGES

47-65

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10998-006-0005-4

DOI

http://dx.doi.org/10.1007/s10998-006-0005-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020114687


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1801", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Law", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/18", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Law and Legal Studies", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Universidad Aut\u00f3noma Metropolitana", 
          "id": "https://www.grid.ac/institutes/grid.7220.7", 
          "name": [
            "Departmento de Matem\u00e1ticas Aplicadas y Sistemas, Universidad Aut\u00f3noma Metropolitana-Cuajimalpa, Prolongaci\u00f3n Canal de Miramontes No. 3855, Col. Ex-Hacienda de San Juan de Dios, Tlalpan 14387 D. F., M\u00e9xico"
          ], 
          "type": "Organization"
        }, 
        "familyName": "P\u00e9rez-Abreu", 
        "givenName": "V\u00edctor", 
        "id": "sg:person.011433753327.87", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011433753327.87"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2006-03", 
    "datePublishedReg": "2006-03-01", 
    "description": "The Gaussian unitary ensemble is a random matrix model (RMM) for the Wigner law. While random matrices in this model are infinitely divisible, the Wigner law is infinitely divisible not in the classical but in the free sense. We prove that any variance mixture of Gaussian distributions -- whether infinitely divisible or not in the classical sense -- admits a RMM of non Gaussian infinitely divisible random matrices. More generally, it is shown that any mixture of the Wigner law admits a RMM. A key role is played by the fact that the Gaussian distribution is the mixture of Wigner law with the ]]>2$-gamma distribution.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10998-006-0005-4", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136293", 
        "issn": [
          "0031-5303", 
          "1588-2829"
        ], 
        "name": "Periodica Mathematica Hungarica", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "52"
      }
    ], 
    "name": "A random matrix model for the Gaussian distribution", 
    "pagination": "47-65", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "5fd6ed751a49d85977fb5ec886e7555835eaa23ec16991a1b841b359cd4de182"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10998-006-0005-4"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1020114687"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10998-006-0005-4", 
      "https://app.dimensions.ai/details/publication/pub.1020114687"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T20:47", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8684_00000512.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs10998-006-0005-4"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10998-006-0005-4'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10998-006-0005-4'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10998-006-0005-4'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10998-006-0005-4'


 

This table displays all metadata directly associated to this object as RDF triples.

61 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10998-006-0005-4 schema:about anzsrc-for:18
2 anzsrc-for:1801
3 schema:author N6e37a1b0bed54e59b4a44310198f898f
4 schema:datePublished 2006-03
5 schema:datePublishedReg 2006-03-01
6 schema:description The Gaussian unitary ensemble is a random matrix model (RMM) for the Wigner law. While random matrices in this model are infinitely divisible, the Wigner law is infinitely divisible not in the classical but in the free sense. We prove that any variance mixture of Gaussian distributions -- whether infinitely divisible or not in the classical sense -- admits a RMM of non Gaussian infinitely divisible random matrices. More generally, it is shown that any mixture of the Wigner law admits a RMM. A key role is played by the fact that the Gaussian distribution is the mixture of Wigner law with the <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>2$-gamma distribution.
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N40d3c361d4dc4e89b60860ee60669e69
11 Na5ff429afbc74810ad58032d86f3a52d
12 sg:journal.1136293
13 schema:name A random matrix model for the Gaussian distribution
14 schema:pagination 47-65
15 schema:productId N87550008918a4e7a8d8a6f7e95a7137c
16 N9510eac6d0e7468db4908331ac656431
17 Nc6a10261e4de4cc59018e1ec677edc82
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020114687
19 https://doi.org/10.1007/s10998-006-0005-4
20 schema:sdDatePublished 2019-04-10T20:47
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher Nb3a33befe9bc4d3e88aa0cb9b67fab38
23 schema:url http://link.springer.com/10.1007%2Fs10998-006-0005-4
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N40d3c361d4dc4e89b60860ee60669e69 schema:volumeNumber 52
28 rdf:type schema:PublicationVolume
29 N6e37a1b0bed54e59b4a44310198f898f rdf:first sg:person.011433753327.87
30 rdf:rest rdf:nil
31 N87550008918a4e7a8d8a6f7e95a7137c schema:name doi
32 schema:value 10.1007/s10998-006-0005-4
33 rdf:type schema:PropertyValue
34 N9510eac6d0e7468db4908331ac656431 schema:name dimensions_id
35 schema:value pub.1020114687
36 rdf:type schema:PropertyValue
37 Na5ff429afbc74810ad58032d86f3a52d schema:issueNumber 1
38 rdf:type schema:PublicationIssue
39 Nb3a33befe9bc4d3e88aa0cb9b67fab38 schema:name Springer Nature - SN SciGraph project
40 rdf:type schema:Organization
41 Nc6a10261e4de4cc59018e1ec677edc82 schema:name readcube_id
42 schema:value 5fd6ed751a49d85977fb5ec886e7555835eaa23ec16991a1b841b359cd4de182
43 rdf:type schema:PropertyValue
44 anzsrc-for:18 schema:inDefinedTermSet anzsrc-for:
45 schema:name Law and Legal Studies
46 rdf:type schema:DefinedTerm
47 anzsrc-for:1801 schema:inDefinedTermSet anzsrc-for:
48 schema:name Law
49 rdf:type schema:DefinedTerm
50 sg:journal.1136293 schema:issn 0031-5303
51 1588-2829
52 schema:name Periodica Mathematica Hungarica
53 rdf:type schema:Periodical
54 sg:person.011433753327.87 schema:affiliation https://www.grid.ac/institutes/grid.7220.7
55 schema:familyName Pérez-Abreu
56 schema:givenName Víctor
57 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011433753327.87
58 rdf:type schema:Person
59 https://www.grid.ac/institutes/grid.7220.7 schema:alternateName Universidad Autónoma Metropolitana
60 schema:name Departmento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana-Cuajimalpa, Prolongación Canal de Miramontes No. 3855, Col. Ex-Hacienda de San Juan de Dios, Tlalpan 14387 D. F., México
61 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...