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Concentration Inequalities: A Nonasymptotic Theory of Independence
Concentration Inequalities: A Nonasymptotic Theory of Independence by Stephane Boucheron, Gabor Lugosi and Pascal Massart
English | 2013 | ISBN: 0199535256 | ISBN-13: 9780199535255 | 480 pages | PDF | 2,3 MB
Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry.
Concentration Compactness for Critical Wave Maps
Concentration Compactness for Critical Wave Maps (EMS Monographs in Mathematics) by Joachim Krieger and Wilhelm Schlag
English | 2012 | ISBN-10: 3037191066 | PDF | 490 pages | 1,9 MB
Wave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric $g$. By Noether's theorem, symmetries of the Lagrangian imply conservation laws for wave maps, such as conservation of energy.
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