# 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.

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:

60G50