Diffusion method in random matrix theory

2016
journal article
article
3
dc.abstract.enWe introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson's Brownian motion and Grassmann/complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the $\beta$ =2 Girko-Ginibre ensembles.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorGrela, Jacek - 195052 pl
dc.date.accessioned2015-12-10T12:49:12Z
dc.date.available2015-12-10T12:49:12Z
dc.date.issued2016pl
dc.description.number1pl
dc.description.publication1,2pl
dc.description.volume49pl
dc.identifier.articleid015201pl
dc.identifier.doi10.1088/1751-8113/49/1/015201pl
dc.identifier.eissn1751-8121pl
dc.identifier.issn1751-8113pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/18048
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subtypeArticlepl
dc.titleDiffusion method in random matrix theorypl
dc.title.journalJournal of Physics. A, Mathematical and Theoreticalpl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
We introduce a calculational tool useful in computing ratios and products of characteristic polynomials averaged over Gaussian measures with an external source. The method is based on Dyson's Brownian motion and Grassmann/complex integration formulas for determinants. The resulting formulas are exact for finite matrix size N and form integral representations convenient for large N asymptotics. Quantities obtained by the method are interpreted as averages over standard matrix models. We provide several explicit and novel calculations with special emphasis on the $\beta$ =2 Girko-Ginibre ensembles.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Grela, Jacek - 195052
dc.date.accessioned
2015-12-10T12:49:12Z
dc.date.available
2015-12-10T12:49:12Z
dc.date.issuedpl
2016
dc.description.numberpl
1
dc.description.publicationpl
1,2
dc.description.volumepl
49
dc.identifier.articleidpl
015201
dc.identifier.doipl
10.1088/1751-8113/49/1/015201
dc.identifier.eissnpl
1751-8121
dc.identifier.issnpl
1751-8113
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/18048
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subtypepl
Article
dc.titlepl
Diffusion method in random matrix theory
dc.title.journalpl
Journal of Physics. A, Mathematical and Theoretical
dc.typepl
JournalArticle
dspace.entity.type
Publication
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