Probability, Geometry and Integrable SystemsMark Pinsky, Bjorn Birnir 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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Contents
Section 1 | 29 |
Section 2 | 53 |
Section 3 | 77 |
Section 4 | 103 |
Section 5 | 110 |
Section 6 | 113 |
Section 7 | 116 |
Section 8 | 117 |
Section 14 | 221 |
Section 15 | 241 |
Section 16 | 252 |
Section 17 | 255 |
Section 18 | 261 |
Section 19 | 287 |
Section 20 | 306 |
Section 21 | 321 |
Section 9 | 120 |
Section 10 | 131 |
Section 11 | 167 |
Section 12 | 185 |
Section 13 | 199 |
Section 22 | 345 |
Section 23 | 356 |
Section 24 | 360 |
Section 25 | 373 |
Section 26 | 397 |
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Common terms and phrases
abelian varieties algebraic Arov and Dym asymptotic Barsotti Birnir Borwein boundary Brownian motions Camia and Newman canonical ensemble coefficients compute concave conformally invariant convergence corresponding Costeniuc curve defined denote differential equations domain eigenvalue elliptic Ellis equilibrium macrostates exists finite flow fluid formula Gaussian ensemble genus given H. P. McKean Hamiltonian initial integral invariant measure inverse KP equation KP solutions Krichever Landen transformation lattice Lemma linear loops Math mathematical matrix microcanonical ensemble mvf's nonequivalence nonlinear Novikov orthogonal polynomials p-moments parameters Phys points potential problem proof random random matrices result Riemann surface Riemann-Hilbert problem rip currents satisfies scaling limit Schrödinger Section shallow water singular solutions SLE6 soliton space statistical stochastic strictly supporting line Theorem theory theta functions turbulence variables vector Vlasov waves white noise