00000cmm a22000004a 4500 UP-99796217611235961 Buklod 20230215085534.0 m go j cr |n |||auu|a 110506s2011 xxu u eng d 9781441995148 (eBook) 1441995137 (eBook) (iLib)UPD-00215705146 DLC DML eng DMLUC QA 188 R33 2011eb Random matrices, random processes and integrable systems [electronic resource] John Harnad ,editor. New York, NY Springer 2011. 1 online resource(xviii, 526 p.) CRM series in mathematical physics IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Mathematical physics. Random matrices. Stochastic processes. Electronic books. Harnad, John. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-1-4419-9514-8 FO Monograph UPD DMLR Electronic Resource