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Probability, Geometry and Integrable Systems

$61.00 (Z)

Part of Mathematical Sciences Research Institute Publications

Damir Arov, Harry Dym, Bjorn Birnir, Anne Boutet de Monvel, Dimtry Shepelsky, Santiago Cambronero, Jose Ramirez, Brian Rider, Federico Camia, Charles M. Newman, Marius Costeniuc, Richard S. Ellis, Hugo Touchette, Bruce Turkington, Paul Malliavin, Ana Bela Cruzeiro, N. M. Ercolani, K. D. T.-R. McLaughlin, J. Gibbons, D. D. Holm, C. Tronci, Petr G. Grinevich, Sergei P. Novikov, F. Alberto Grunbaum, Enrique Loubet, Dante V. Manna, Victor H. Moll, Emma Previato, Harvey Segur, Pierre Van Moerbeke, S. R. S. Varadhan
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  • Date Published: February 2011
  • availability: Manufactured on demand: supplied direct from the printer
  • format: Paperback
  • isbn: 9780521175401

$61.00 (Z)
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About the Authors
  • 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.

    • Novel interplay between different mathematical topics
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    Reviews & endorsements

    "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 17 papers included here demonstrate a variety of techniques that have been developed to solve various mathematical problems in these areas. The topics are often combined in an unusual fashion to give solutions outside of the standard methods. A few specific topics explored are stochastic evolution of inviscid Burger fluid, singular solutions for geodesic flows of Vlasov moments, and reality problems in soliton theory." --Book News

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    Product details

    • Date Published: February 2011
    • format: Paperback
    • isbn: 9780521175401
    • length: 428 pages
    • dimensions: 234 x 156 x 22 mm
    • weight: 0.6kg
    • availability: Manufactured on demand: supplied direct from the printer
  • Table of Contents

    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.

  • Editors

    Mark Pinsky, Northwestern University, Illinois

    Bjorn Birnir, University of California, Santa Barbara

    Contributors

    Damir Arov, Harry Dym, Bjorn Birnir, Anne Boutet de Monvel, Dimtry Shepelsky, Santiago Cambronero, Jose Ramirez, Brian Rider, Federico Camia, Charles M. Newman, Marius Costeniuc, Richard S. Ellis, Hugo Touchette, Bruce Turkington, Paul Malliavin, Ana Bela Cruzeiro, N. M. Ercolani, K. D. T.-R. McLaughlin, J. Gibbons, D. D. Holm, C. Tronci, Petr G. Grinevich, Sergei P. Novikov, F. Alberto Grunbaum, Enrique Loubet, Dante V. Manna, Victor H. Moll, Emma Previato, Harvey Segur, Pierre Van Moerbeke, S. R. S. Varadhan

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