Geometric Aspects of Functional Analysis Israel Seminar (GAFA) 2011-2013 [Paperback]

As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and log-concave measures in high-dimensions and in particular the mean-norm, mean-width, metric entropy, spectral-gap, thin-shell and slicing parameters, with applications to Dvoretzky and Central-Limit-type results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixed-volumes. The interplay between the real convex and complex pluri-subharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.

Dominique Bakry and Marguerite Zani: Random symmetric matrices on Clifford algebras.- Itai Benjamini: Gaussian free field on hyperbolic lattices.- Itai Benjamini and Pascal Maillard: Point-to-point distance in first passage percolation on (tree)Z.- Zbigniew Blocki: A lower bound for the Bergman kernel and the Bourgain-Milman inequality.- Jean Bourgain: An improved estimate in the restricted isometry problem.- Jean Bourgain: On eigenvalue spacings for the 1-D Anderson model with singular site distribution.- Jean Bourgain: On the local eigenvalue spacings for certain Anderson-Bernoulli Hamiltonians.- Jean Bourgain: On the control problem for Schrodinger operators on tori.- Ronen Eldan and Joseph Lehec: Bounding the norm of a log-concave vl0