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Asymptotic Expansion of a Partition Function Related to the Sinh-model
This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Colección: | Mathematical Physics Studies,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-319-33379-3 | ||
| 003 | DE-He213 | ||
| 005 | 20220116191231.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 161210s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783319333793 |9 978-3-319-33379-3 | ||
| 024 | 7 | |a 10.1007/978-3-319-33379-3 |2 doi | |
| 050 | 4 | |a QC19.2-20.85 | |
| 072 | 7 | |a PHU |2 bicssc | |
| 072 | 7 | |a SCI040000 |2 bisacsh | |
| 072 | 7 | |a PHU |2 thema | |
| 082 | 0 | 4 | |a 530.15 |2 23 |
| 100 | 1 | |a Borot, Gaëtan. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Asymptotic Expansion of a Partition Function Related to the Sinh-model |h [electronic resource] / |c by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2016. | |
| 300 | |a XV, 222 p. 4 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Mathematical Physics Studies, |x 2352-3905 | |
| 505 | 0 | |a Introduction -- Main results and strategy of proof -- Asymptotic expansion of ln ZN[V], the Schwinger-Dyson equation approach -- The Riemann-Hilbert approach to the inversion of SN -- The operators WN and U-1N -- Asymptotic analysis of integrals -- Several theorems and properties of use to the analysis -- Proof of Theorem 2.1.1 -- Properties of the N-dependent equilibrium measure -- The Gaussian potential -- Summary of symbols. | |
| 520 | |a This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields. | ||
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Potential theory (Mathematics). | |
| 650 | 0 | |a System theory. | |
| 650 | 1 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Potential Theory. |
| 650 | 2 | 4 | |a Complex Systems. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Theoretical, Mathematical and Computational Physics. |
| 700 | 1 | |a Guionnet, Alice. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Kozlowski, Karol K. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319333786 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319333809 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319814995 |
| 830 | 0 | |a Mathematical Physics Studies, |x 2352-3905 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-33379-3 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||