Probability, Geometry and Integrable Systems - Brossura

Pinsky, Mark

Brossura

ISBN 10: 0521175402 ISBN 13: 9780521175401

Casa editrice: Cambridge University Press, 2011

Riassunto

The three main themes of this book, probability theory, differential geometry, and the theory of integrable systems, reflect the broad range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the seventeen papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems in these areas. The topics are often combined in an unusual and interesting fashion to give solutions outside of the standard methods. The papers contain some exciting results and offer a guide to the contemporary literature on these subjects.

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Descrizione del libro

The three main themes of this book reflect the range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the papers here demonstrate a variety of techniques for solving problems, often outside of the standard methods.

Contenuti

1. Direct and inverse problems for systems of differential equations Damir Arov and Harry Dym; 2. Turbulence of a unidirectional flow Bjorn Birnir; 3. Riemann–Hilbert problem in the inverse scattering for the Camassa–Holm equation on the line Anne Boutet de Monvel and Dimtry Shepelsky; 4. The Riccati map in random Schrodinger and matrix theory Santiago Cambronero, Jose Ramirez and Brian Rider; 5. SLE6 and CLE6 from critical percolation Federico Camia and Charles M. Newman; 6. Global optimization, the gaussian ensemble and universal ensemble equivalence Marius Costeniuc, Richard S. Ellis, Hugo Touchette and Bruce Turkington; 7. Stochastic evolution of inviscid Burger fluid Paul Malliavin and Ana Bela Cruzeiro; 8. A quick derivation of the loop equations for random matrices N. M. Ercolani and K. D. T.-R. McLaughlin; 9. Singular solutions for geodesic flows of Vlasov moments J. Gibbons, D. D. Holm and C. Tronci; 10. Reality problems in soliton theory Petr G. Grinevich and Sergei P. Novikov; 11. Random walks and orthogonal polynomials; some challenges F. Alberto Grunbaum; 12. Integration of pair flows of the Camassa–Holm hierarchy Enrique Loubet; 13. Landen survey Dante V. Manna and Victor H. Moll; 13. Lines on abelian varieties Emma Previato; 14. Integrable models of waves in shallow water Harvey Segur; 15. Nonintersecting brownian motions, integrable systems and orthogonal polynomials Pierre Van Moerbeke; 16. Homogenization of random Hamilton–Jacobi–Bellman equations S. R. S. Varadhan.

Dettagli dell?edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2011
• ISBN 10: 0521175402
• ISBN 13: 9780521175401
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 428