Banach September 2004

banach@mathdept.okstate.edu

2 participants
2 discussions

announcement Winter School, Toulouse 2005
by ledoux＠math.ups-tlse.fr 27 Sep '04

27 Sep '04

Dear colleagues, would it be possible to announce on the Banach Bulletin Board the second announcement (below) of the Winter School on Probabilistic Methods in High Dimension Phenomena? Many thanks in advance for your help. Sincerely yours. M. Ledoux ----------------------------------------------------------------------------- Second Announcement of the Winter School on PROBABILISTIC METHODS IN HIGH DIMENSION PHENOMENA Toulouse, January 10-14, 2005 The school will provide young as well as expert scientists with the recent probabilistic tools developed for the investigation of high-dimensional systems. It is part of the European Network "Phenomena in High Dimension". It will be composed of the following five courses: I.Benjamini (Rehovot) ``Random walks and Percolation on graphs'' C.Borell (Goteborg) ``Minkowski sums in Gaussian analysis'' K.Johansson (Stockholm) ``Determinantal Processes in Random Matrix Theory'' G.Lugosi (Barcelona) ``Concentration of Functions of Independent Random Variables'' R.Schneider (Freiburg) ``Convexity in Stochastic Geometry'' It is now time for participants: * to registrate: we had some technical problems with the online registration engine. So we ask you to registrate (to REGISTRATE AGAIN if you already did it through the online form) by sending an email to our secretary Mrs Michel michel(a)lsp.ups-tlse.fr, specifying your NAME, your AFFILIATION, ADDRESS and DATES of attendance. * and to prepare their travel and accomodation plans: The expenses of the members of the PHD network are supported by their nodes (but it is likely that universities have to pay in advance and the RTN will reimburse when it is operating). We hope that we will have some money left to partially cover the expenses of participants not belonging to the network. Priority will be given to PHD Students and Post-Docs. If you need such support, please mention it in the registration email to Mrs Michel. More information is available on the conference Webpage http://www.lsp.ups-tlse.fr/Proba_Winter_School/ It has been updated and contains new pieces of information about * abstracts of the courses * accomodation: The list of hotels has been completed. Economical options have been added. In particular we have made a temporary reservation for a very limited number of rooms on the campus for 22 Euros per night. These rooms can be booked by sending an email to Mrs Michel (michel(a)lesp.ups-tlse.fr). Sincerely, F. Barthe M. Ledoux ------------------------------------------------------------------------------ Institut de Mathematiques - Universite Paul Sabatier - Toulouse III 118 route de Narbonne - 31062 Toulouse Cedex 4 - FRANCE. __________________________________________________________________________ Michel Ledoux ledoux(a)math.ups-tlse.fr Institut de Mathematiques Tel : (+33) 561 55 85 74 Universite de Toulouse Fax : (+33) 561 55 60 89 F-31062 Toulouse, France http://www.lsp.ups-tlse.fr/Ledoux/

1 0

Abstract of a paper by Narcisse Randrianantoanina
by Dale Alspach 09 Sep '04

09 Sep '04

This is an announcement for the paper "A weak-type inequality for non-commutative martingales and applications" by Narcisse Randrianantoanina. Abstract: We prove a weak-type (1,1) inequality for square functions of non-commutative martingales that are simultaneously bounded in $L^2$ and $L^1$. More precisely, the following non-commutative analogue of a classical result of Burkholder holds: there exists an absolute constant $K>0$ such that if $\cal{M}$ is a semi-finite von Neumann algebra and $(\cal{M}_n)^{\infty}_{n=1}$ is an increasing filtration of von Neumann subalgebras of $\cal{M}$ then for any given martingale $x=(x_n)^{\infty}_{n=1}$ that is bounded in $L^2(\cal{M})\cap L^1(\cal{M})$, adapted to $(\cal{M}_n)^{\infty}_{n=1}$, there exist two \underline{martingale difference} sequences, $a=(a_n)_{n=1}^\infty$ and $b=(b_n)_{n=1}^\infty$, with $dx_n = a_n + b_n$ for every $n\geq 1$, \[ \left\| \left(\sum^\infty_{n=1} a_n^*a_n \right)^{{1}/{2}}\right\|_{2} + \left\| \left(\sum^\infty_{n=1} b_nb_n^*\right)^{1/2}\right\|_{2} \leq 2\left\| x \right\|_2, \] and \[ \left\| \left(\sum^\infty_{n=1} a_n^*a_n \right)^{{1}/{2}}\right\|_{1,\infty} + \left\| \left(\sum^\infty_{n=1} b_nb_n^*\right)^{1/2}\right\|_{1,\infty} \leq K\left\| x \right\|_1. \] As an application, we obtain the optimal orders of growth for the constants involved in the Pisier-Xu non-commutative analogue of the classical Burkholder-Gundy inequalities. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L53, 46L52 Remarks: 38 pages The source file(s), weaktype4.tex: 108231 bytes, is(are) stored in gzipped form as 0409139.gz with size 30kb. The corresponding postcript file has gzipped size 137kb. Submitted from: randrin(a)muohio.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0409139 or http://arXiv.org/abs/math.FA/0409139 or by email in unzipped form by transmitting an empty message with subject line uget 0409139 or in gzipped form by using subject line get 0409139 to: math(a)arXiv.org.

1 0

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach September 2004