Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Are there results/techniques pertaining to the analysis of squares of random matrices ?

More specifically, let $A$ be an $n\times n$ matrix such that each entry is $1$ or $-1$ independently and with equal probability. Now if we want to analyze for any $u,v \in \{-1,1\}^n$, we can make a case for concentration of the value of $u^TAv$ using chernoff bound arguements. However suppose now we want to analyze the value of $u^TA^2v$. This time due to a lot of dependencies among the variables a chernoff type arguement becomes difficult or at least I cannot see it straightaway. Could someone point me to an analysis for this scenario ?

share|cite|improve this question
I am a fan of these matrices as connecting physics with number theory, but honestly I saw yet no literature on their squares. Interesting! – al-Hwarizmi Jun 14 '13 at 17:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.