Probability, Geometry and Integrable Systems

by Mark Pinsky, Bjorn Birnir

Overview

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.

Product Details

ISBN-13:	9780521175401
Publisher:	Cambridge University Press
Publication date:	02/17/2011
Series:	Mathematical Sciences Research Institute Publications , #55
Edition description:	Reissue
Pages:	428
Product dimensions:	6.10(w) x 9.10(h) x 1.00(d)

About the Author

Mark Pinsky is Professor of Mathematics at Northwestern University, where he has been since 1968, following a two-year postdoctoral position at Stanford. He completed his PhD at MIT in 1966, under the direction of Henry McKean. His published work includes 125 research papers and 10 books, including several conference proceedings and textbooks. His most recent book, Introduction to Fourier Analysis and Wavelets, has been translated into Spanish. Pinsky is a member of the AMS, IMS, and MAA and has published in their journals and served on various committees, most recently as Consulting Editor for the AMS. He served on the Executive Committee of MSRI for the period 1996-2000. His current interests include classical harmonic analysis and stochastic Riemannian geometry.

Björn Birnir is a Professor of Mathematics at the University of California at Santa Barbara (UCSB). He served as the UCSB coordinator for nonlinear science from 1985-1990. He is currently the director of the Center for Complex and Nonlinear Science at UC Santa Barbara. His current research interests are: Stochastic nonlinear partial differential equations (SPDEs) and turbulence, dynamical systems theory of nonlinear partial differential equations, mathematical seismology and geomorphology, nonlinear phenomena in quantum mechanical systems, complex and nonlinear models in biology, and applications of the above. He is the author of more than 70 publications.

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.

Editorial Reviews

"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

From the Publisher