http://tcsmath.wordpress.com/2008/05/14/the-cheeger-alon-milman-inequality/ some mathematics of theoretical computer science Fri, 16 Oct 2009 11:37:51 +0000 http://wordpress.com/ hourly 1 http://tcsmath.wordpress.com/2008/05/14/the-cheeger-alon-milman-inequality/#comment-72 Lecture 2: Spectral partitioning and near-optimal foams « tcs math - some mathematics of theoretical computer science Fri, 26 Sep 2008 09:12:46 +0000 http://tcsmath.wordpress.com/?p=45#comment-72 [...] For the proof, I’ll refer to Theorem 4 in Alon-Klartag.  Note that the proof for the Dirichlet version is even simpler than for the “standard” (Neumann) eigenvalues—it’s just a straightforward combination of Cauchy-Schwarz and the coarea formula. [...] [...] For the proof, I’ll refer to Theorem 4 in Alon-Klartag.  Note that the proof for the Dirichlet version is even simpler than for the “standard” (Neumann) eigenvalues—it’s just a straightforward combination of Cauchy-Schwarz and the coarea formula. [...]

]]> http://tcsmath.wordpress.com/2008/05/14/the-cheeger-alon-milman-inequality/#comment-28 Eigenvalue multiplicity and growth of groups « tcs math - some mathematics of theoretical computer science Sun, 15 Jun 2008 16:25:01 +0000 http://tcsmath.wordpress.com/?p=45#comment-28 [...] group in terms of on . But on a small, connected graph cannot be too close to zero by the discrete Cheeger inequality. In this way, we arrive at a contradiction if the image of the action is too small. Theorem 2 [...] [...] group in terms of on . But on a small, connected graph cannot be too close to zero by the discrete Cheeger inequality. In this way, we arrive at a contradiction if the image of the action is too small. Theorem 2 [...]

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