🔖 The Entropy Decrement Method and the Erdos Discrepancy Problem | Simons Institute for the Theory of Computing

Tuesday, April 11th, 2017 9:30 am – 10:30 am
Structure vs. Randomness
Speaker: Terry Tao, UCLA

We discuss a variant of the density and energy increment arguments that we call an "entropy decrement method", which can be used to locate a scale in which two relevant random variables share very little mutual information, and thus behave somewhat like independent random variables.  We were able to use this method to obtain a new correlation estimate for multiplicative functions, which in turn was used to establish the Erdos discrepancy conjecture that any sequence taking values in {-1,+1} had unbounded sums on homogeneous arithmetic progressions.