Banach November 2009

banach@mathdept.okstate.edu

2 participants
8 discussions

Abstract of a paper by Daniel A. Spielman and Nikhil Srivastava
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "An elementary proof of the Restricted Invertibility Theorem" by Daniel A. Spielman and Nikhil Srivastava. Abstract: We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace. Archive classification: math.FA The source file(s), restrict.tex: 13698 bytes, is(are) stored in gzipped form as 0911.1114.gz with size 5kb. The corresponding postcript file has gzipped size 58kb. Submitted from: nikhil.srivastava(a)yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.1114 or http://arXiv.org/abs/0911.1114 or by email in unzipped form by transmitting an empty message with subject line uget 0911.1114 or in gzipped form by using subject line get 0911.1114 to: math(a)arXiv.org.

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Abstract of a paper by Elisabeth M. Werner and Deping Ye
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "On the Homothety Conjecture" by Elisabeth M. Werner and Deping Ye. Abstract: Let $K$ be a convex body in $\bbR^n$ and $\d>0$. The homothety conjecture asks: Does $K_{\d}=c K$ imply that $K$ is an ellipsoid? Here $K_{\d}$ is the (convex) floating body and $c$ is a constant depending on $\d$ only. In this paper we prove that the homothety conjecture holds true in the class of the convex bodies $B^n_p$, $1\leq p\leq \infty$, the unit balls of $l_p^n$; namely, we show that $(B^n_p)_{\d} = c B^n_p$ if and only if $p=2$. We also show that the homothety conjecture is true for a general convex body $K$ if $\d$ is small enough. This improvs earlier results by Sch\"utt and Werner \cite{SW1994} and Stancu \cite{Stancu2009}. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Remarks: 24 pages, 2 figures The source file(s), floating-2.jpg: 38222 bytes floating.jpg: 27480 bytes homothety102609.tex: 58622 bytes, is(are) stored in gzipped form as 0911.0642.tar.gz with size 68kb. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0642 or http://arXiv.org/abs/0911.0642 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0642 or in gzipped form by using subject line get 0911.0642 to: math(a)arXiv.org.

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Abstract of a paper by Roman Vershynin
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Approximating the moments of marginals of high dimensional distributions" by Roman Vershynin. Abstract: For probability distributions on R^n, we study the optimal sample size N=N(n,p) that suffices to uniformly approximate the p-th moments of all one-dimensional marginals. Under the assumption that the support of the distribution lies in the Euclidean ball of radius \sqrt{n} and the marginals have bounded 4p moments, we obtain the optimal bound N = O(n^{p/2}) for p > 2. This bound goes in the direction of bridging the two recent results: a theorem of Guedon and Rudelson which has an extra logarithmic factor in the sample size, and a recent result of Adamczak, Litvak, Pajor and Tomczak-Jaegermann which requires stronger subexponential moment assumptions. Archive classification: math.PR math.FA Mathematics Subject Classification: 46B09; 52A21; 62J10 Remarks: 12 pages The source file(s), moments-of-marginals.tex: 32410 bytes, is(are) stored in gzipped form as 0911.0391.gz with size 11kb. The corresponding postcript file has gzipped size 92kb. Submitted from: romanv(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0391 or http://arXiv.org/abs/0911.0391 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0391 or in gzipped form by using subject line get 0911.0391 to: math(a)arXiv.org.

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Abstract of a paper by A. J. Scott and M. Grassl
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "SIC-POVMs: A new computer study" by A. J. Scott and M. Grassl. Abstract: We report on a new computer study into the existence of d^2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the underlying mathematical objects defining symmetric informationally complete measurements in quantum theory. We provide numerical solutions in all dimensions d <= 67 and, moreover, a putatively complete list of Weyl-Heisenberg covariant solutions for d <= 50. A symmetry analysis of this list leads to new algebraic solutions in dimensions d = 24, 35 and 48, which are given together with algebraic solutions for d = 4,..., 15 and 19. Archive classification: quant-ph math.CO math.FA Remarks: 20 pages + 189 pages of raw data (also accessible in the source in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.5784 or http://arXiv.org/abs/0910.5784 or by email in unzipped form by transmitting an empty message with subject line uget 0910.5784 or in gzipped form by using subject line get 0910.5784 to: math(a)arXiv.org.

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Abstract of a paper by Roland Speicher
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Free probability theory" by Roland Speicher. Abstract: Free probability theory was created by Dan Voiculescu around 1985, motivated by his efforts to understand special classes of von Neumann algebras. His discovery in 1991 that also random matrices satisfy asymptotically the freeness relation transformed the theory dramatically. Not only did this yield spectacular results about the structure of operator algebras, but it also brought new concepts and tools into the realm of random matrix theory. In the following we will give, mostly from the random matrix point of view, a survey on some of the basic ideas and results of free probability theory. Archive classification: math.PR math.OA Remarks: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press The source file(s), RMT-chapter22.tex: 56575 bytes wignerpluswishart.ps: 11793 bytes wisharttimeswishart.ps: 10691 bytes, is(are) stored in gzipped form as 0911.0087.tar.gz with size 23kb. The corresponding postcript file has gzipped size 119kb. Submitted from: speicher(a)mast.queensu.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0087 or http://arXiv.org/abs/0911.0087 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0087 or in gzipped form by using subject line get 0911.0087 to: math(a)arXiv.org.

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Abstract of a paper by Paul F.X. Mueller
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Two remarks on primary spaces" by Paul F.X. Mueller. Abstract: We prove that for any operator $T$ on $ \ell^\infty( H^1 (\bT)) ,$ the identity factores through $ T $ or $ \Id - T .$ We re-prove analogous results of H.M. Wark for the spaces $ \ell^\infty(H^p(\bT) ), $ $1<p <\infty .$ In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemeredi's theorem in the work of H. M. Wark. \\ Archive classification: math.FA Mathematics Subject Classification: 46B25, 46E40 The source file(s), buch.def: 1005 bytes math111.def: 7238 bytes primary.bbl: 2310 bytes primary.tex: 40643 bytes, is(are) stored in gzipped form as 0911.0074.tar.gz with size 16kb. The corresponding postcript file has gzipped size 107kb. Submitted from: pfxm(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0074 or http://arXiv.org/abs/0911.0074 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0074 or in gzipped form by using subject line get 0911.0074 to: math(a)arXiv.org.

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Abstract of a paper by Joris Bierkens and Onno van Gaans
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Stochastic integration in Banach spaces using a product structure with partial order" by Joris Bierkens and Onno van Gaans. Abstract: Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales. Archive classification: math.PR math.FA Mathematics Subject Classification: 60H05 The source file(s), reportdec06.tex: 91221 bytes, is(are) stored in gzipped form as 0910.5363.gz with size 21kb. The corresponding postcript file has gzipped size 154kb. Submitted from: j.bierkens(a)cwi.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.5363 or http://arXiv.org/abs/0910.5363 or by email in unzipped form by transmitting an empty message with subject line uget 0910.5363 or in gzipped form by using subject line get 0910.5363 to: math(a)arXiv.org.

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INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 12 Nov '09

12 Nov '09

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date March 19/ Departure March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL It would be great if you could visit Kent State and participate in the seminar! May we ask you to respond as soon as possible (zvavitch(a)math.kent.edu), so that we can gauge the need for housing, lecture room(s), etc. We hope to be sending out information regarding tiles/abstracts/housing by the middle of December 2009. Best Regards, Analysis group at Kent State!

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Banach November 2009