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比利时vs摩洛哥足彩 ,
university of california san diego

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math 262 - reading in combinatorics

kevin costello and prof. van vu

ucsd

singularity of random matrices

abstract:

let $m_n$ be a random matrix whose entries are i.i.d bernoulli random variables and $q_n$ be a random symmetric matrix whose upper diagonal entries are i.i.d bernoulli random variables. we prove: \vskip .1in \noindent 1. p ($q_n$ is singular)$= 0$($n^{-1/8+ \epsilon }$) (costello, tao and vu). \vskip .1in \noindent 2. p($m_n$ is singular)$=0$ (($3/4$)$^n$) (tao and vu). \vskip .1in \noindent the first result answers a question of b. weiss, posed in the early 1990s. the second improved an earlier bound ($.999^n$) of kahn, komlos and szemeredi from 1995. \vskip .1in \noindent from 2:00 p.m. to 2:30 p.m., costello will talk about ($1$). vu will continue from 3 p.m. to 3:30 p.m. with the beginning of the proof of ($2$). the rest of the proof comes next week.

host:

may 24, 2005

2:00 pm

ap&m 6218

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