An Introduction to Inverse Littlewood-Offord Theory

Monday, September 29, 2014 - 9:00am - 9:50am
Keller 3-180
Terence Tao (University of California, Los Angeles)
Littlewood-Offord theory is the study of random signed sums
of n integers (or more generally, vectors), being particularly
concerned with the probability that such a sum equals a fixed value
(such as zero) or lies in a fixed set (such as the unit ball).
Inverse Littlewood-Offord theory starts with some information about
such probabilities (e.g. that a signed sum equals 0 with high
probability) and deduces structural information about the original
spacings (typically, that they are largely contained within a
progression). We give examples of such theorems and describe some of
the applications to random matrix theory. Our focus will be on the
simplest applications, rather than the most recent ones.
MSC Code: