Lecture11

Lecture11 - Lecture 11: A Local Cheeger Inequality Using...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 11: A Local Cheeger Inequality Using Lazy Walks Transcriber: Franklin Kenter The goal of this lecture is to prove an inequality involving h S , the Cheeger constant using the Dirchelet eigenvalues. Goal Theorem: h S S 2 4- log | S | t Definition of : = min u S { h f : f u Z k ,k t,f : V [0 , ) , k f k 1 = 1 } That is, we can bound the Cheeger constant for a given subset, h S without actually necessarily computing the Dirchelet eigenvalues. But instead, we can find a good enough cut using the lazy walk to bound S , and hence, h S . Secton 1: The Extensions of f In order to prove the theorem, we will, first, provide from extensions of f . Below we will use a subscript for each of the extensions. However, afterwards, since all of the extensions have different domains, we plan to abuse notation and remove the subscripts. First Extension: f on the edges of G f E : V V [0 , ) defined as f ( u,v ) = f ( u ) d u 1 u v Note that f E is not symmetric. Also, note f E is defined on non-edges to be 0....
View Full Document

This note was uploaded on 09/30/2011 for the course MATH 262 taught by Professor Aterras during the Fall '08 term at UCSD.

Page1 / 4

Lecture11 - Lecture 11: A Local Cheeger Inequality Using...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online