On the function TreH+itK
We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace τ, that the function t∈ℝ↦τ(exp(a+itb)) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011468 |
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| _version_ | 1832546091579473920 |
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| author | Mark Fannes Dénes Petz |
| author_facet | Mark Fannes Dénes Petz |
| author_sort | Mark Fannes |
| collection | DOAJ |
| description | We prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace τ, that the function t∈ℝ↦τ(exp(a+itb)) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense. |
| format | Article |
| id | doaj-art-da007c479eb74fdebb368592e281be08 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-da007c479eb74fdebb368592e281be082025-02-03T07:23:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129738939310.1155/S0161171202011468On the function TreH+itKMark Fannes0Dénes Petz1Instituut voor Theoretische Fysika, Katholieke Universiteit Leuven, Leuven B-3001, BelgiumDepartment for Mathematical Analysis, Budapest University of Technology and Economics, Budapest XI. H-1521, HungaryWe prove, for two free semicircularly distributed selfadjoint elements a and b in a type II1 von Neumann algebra with faithful trace τ, that the function t∈ℝ↦τ(exp(a+itb)) is positive definite. This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.http://dx.doi.org/10.1155/S0161171202011468 |
| spellingShingle | Mark Fannes Dénes Petz On the function TreH+itK International Journal of Mathematics and Mathematical Sciences |
| title | On the function TreH+itK |
| title_full | On the function TreH+itK |
| title_fullStr | On the function TreH+itK |
| title_full_unstemmed | On the function TreH+itK |
| title_short | On the function TreH+itK |
| title_sort | on the function treh itk |
| url | http://dx.doi.org/10.1155/S0161171202011468 |
| work_keys_str_mv | AT markfannes onthefunctiontrehitk AT denespetz onthefunctiontrehitk |