Probability, Geometry and Integrable Systems

Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.

Mark Pinsky (Edited by), Bjorn Birnir (Edited by)

9780521175401, Cambridge University Press

Paperback, published 17 February 2011

428 pages
23.4 x 15.6 x 2.2 cm, 0.6 kg

"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

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]