01742nam a2200337 i 4500991000498389707536040301s2003 enka 000 0 eng d0521531624b12625863-39ule_instDip.to Matematicaeng51621LC QA446.C48AMS 51-06The changing shape of geometry :celebrating a century of geometry and geometry teaching /edited on behalf of the Mathematical Association by Chris PritchardCambridge ; New York :Cambridge University Press,2003xviii, 541 p. :ill. ;26 cmSpectrum seriesIncludes bibliographical referencesPt. 1.: The nature of geometry ; Desert island theorems group A: Greek geometry ; pt. 2.: The history of geometry ; Desert island theorems group B: Elementary Euclidean geometry ; pt. 3.: Pythagoras' theorem ; Desert island theorems group C: Advanced Euclidean geometry ; pt. 4. The golden ratio ; Desert island theorems group D: Non-Euclidean geometry & topology ; pt. 5.: Recreational geometry ; Desert island theorems group E: Geometrical physics ; pt. 6.: The teaching of geometry.GeometryGeometryHistoryGeometryProblemsMathematical recreationsPritchard, ChrisMathematical Association of America.b1262586306-09-1201-03-04991000498389707536LE013 51-XX PRI11 (2003)12013000144665le013pE38.38-l- 04040.i1320414217-03-04Changing shape of geometry277373UNISALENTOle01301-03-04ma -engenk4104585nam 22007455 450 991015530550332120251117002217.03-319-33379-810.1007/978-3-319-33379-3(CKB)4340000000024354(DE-He213)978-3-319-33379-3(MiAaPQ)EBC4768144(PPN)197455417(EXLCZ)99434000000002435420161210d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierAsymptotic expansion of a partition function related to the sinh-model /by Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XV, 222 p. 4 illus.)Mathematical Physics Studies,0921-37673-319-33378-X Includes bibliographical references at the end of each chapters and index.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.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.Mathematical Physics Studies,0921-3767Mathematical physicsProbabilitiesPotential theory (Mathematics)Statistical physicsDynamicsPhysicsMathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Mathematical physics.Probabilities.Potential theory (Mathematics)Statistical physics.Dynamics.Physics.Mathematical Physics.Probability Theory and Stochastic Processes.Potential Theory.Complex Systems.Mathematical Methods in Physics.Statistical Physics and Dynamical Systems.510Borot Gaëtanauthttp://id.loc.gov/vocabulary/relators/aut755840Guionnet Aliceauthttp://id.loc.gov/vocabulary/relators/autKozlowski Karol K.authttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910155305503321Asymptotic Expansion of a Partition Function Related to the Sinh-model2108049UNINA