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Dan Romik - The Surprising Mathematics of Longest Increasing Subsequences, Häftad

Häftad, Engelska, 2015

Del 4 i serien Institute of Mathematical Statistics Textbooks

The Surprising Mathematics of Longest Increasing Subsequences

Av Dan Romik

989 kr

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Beskrivning
In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.
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Dan Romik is Professor of Mathematics at the University of California, Davis.

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'The story of longest monotone subsequences in permutations has been, for six decades, one of the most beautiful in mathematics, ranging from the very pure to the applied and featuring many terrific mathematicians, starting with Erdős–Szekeres's 'happy end theorem' and continuing through the Tracy–Widom distribution and the breakthrough of Baik–Deift–Johansson. With its connections to many areas of mathematics, to the Riemann hypothesis, and to high-energy physics we cannot foresee where the story is heading. Dan Romik tells the tale thus far - and teaches its rich multifaceted mathematics, a blend of probability, combinatorics, analysis, and algebra - in a wonderful way.' Gil Kalai, Hebrew University of Jerusalem

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