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SUMMARY:Noise sensitivity of Boolean functions - Edward Mottram (CCA)
DTSTART:20130612T150000Z
DTEND:20130612T160000Z
UID:TALK44747@talks.cam.ac.uk
CONTACT:Martin Taylor
DESCRIPTION:A Boolean function is a function from the hypercube {-1\,1}^n 
 into {-1\,1}.  Basic examples include the dictatorship function DICT(x_1\,
 ...x_n) = x_1 and the parity function PAR(x_1\,...\,x_n) = x_1*...*x_n.  W
 e consider the effect of perturbing x_1\,...\,x_n by some small random noi
 se.  Clearly one would expect the dictatorship function to remain unchange
 d and the parity function to be almost independent from before.  Our main 
 interest is in Boolean functions arising in the percolation model where th
 e effect of a random noise is less obvious.  We shall see that phenomenon 
 of noise sensitivity is related to the energy spectrum of a function.  Thu
 s Fourier analysis gives us a powerful tool for studying the affects of ra
 ndom noise on a percolation configuration.
LOCATION:MR14\, Centre for Mathematical Sciences
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