Summary: Com S 633: Randomness in Computation
Lectures 19 and 20 Scribe: Ankit Agrawal, Dave Doty
Rakesh Setty
Let G be a connected d-regular non-bipartite graph. Let M be its corresponding normal-
ized adjacency matrix and let v 1 ; v 2 ; : : : v n be the corresponding eigenbasis where,
v 1 =
 1
p
n
; 1
p
n
; : : : 1
p
n

Let  1 ;  2 ; : : :  n be the corresponding eigenvalues such that
 1 = 1 and
 1 > j 2 j  : : : j n j
We will denote j 2 j with . In the last class, we showed that for any distribution 

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

Collections: Computer Technologies and Information Sciences