#55:
Probability, Geometry and Integrable Systems
**Up:** MSRI Publications

# MSRI Publications – Volume 55

## Probability, Geometry and Integrable Systems

For Henry McKean's Seventy-Fifth Birthday

### Edited by
Mark Pinsky and
Björn Birnir

### Contents

Front matter (front page, copyright page)

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Table of Contents

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Preface, ix-xiv

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A tribute to Henry McKean by the Editors, xv-xxiii

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Direct and inverse problems for systems of differential equations,
by **Damir Arov and Harry Dym**, 1-28

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Turbulence of a unidirectional flow,
by **Björn Birnir**, 29-52

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Riemann--Hilbert problem in the inverse scattering for the
Camassa--Holm equation on the line,
by **Anne Boutet de Monvel and Dmitry Shepelsky**, 53-75

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The Riccati map in random Schröodinger and matrix theory,
by **Santiago Cambronero, José Ramírez and Brian Rider**, 77-101

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SLE_{6} and CLE_{6} from critical percolation,
by **Federico Camia and Charles M. Newman**, 103-130

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Global optimization, the Gaussian ensemble and universal
ensemble equivalence,
by **Marius Costeniuc, Richard S. Ellis, Hugo Touchette and Bruce Turkington**, 131-165

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Stochastic evolution of inviscid Burger fluid,
by **Ana Bela Cruzeiro and Paul Malliavin**, 167-183

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A quick derivation of the loop equations for random matrices,
by **N. M. Ercolani and K. D. T-R McLaughlin**, 185-198

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Singular solutions for geodesic flows of Vlasov moments,
by **J. Gibbons, D. D. Holm and C. Tronci**, 199-220

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Reality problems in soliton theory,
by **Petr G. Grinevich and Sergei P. Novikov**, 221-239

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Random walks and orthogonal polynomials; some challenges,
by **F. Alberto Grüunbaum**, 241-260

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Integration of pair flows of the Camassa--Holm hierarchy,
by **Enrique Loubet**, 261-285

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Landen survey,
by **Dante V. Manna and Victor H. Moll**, 287-319

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Lines on abelian varieties,
by **Emma Previato**, 321-344

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Integrable models of waves in shallow water,
by **Harvey Segur**, 345-371

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Rip
current animation

Animation
of KP solutions

Nonintersecting Brownian motions, integrable systems and
orthogonal polynomials,
by **Pierre van Moerbeke**, 373-396

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Homogenization of random Hamilton--Jacobi--Bellman equations,
by **S. R. Srinivasa Varadhan**, 397-403

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