We will discuss a new paper of Alfonso Bandeira, Asaf Ferber and Matthew Kwan. It presents a different view on a classical anti-concentration problem. Classical Littlewood-Offord gives an upper bound for the concentration of the linear combinations \sum_{i=1}^n a_i*x_i, where a = (a_i) is a fixed vector and x = (x_i) is a sequence of i.i.d. random variables.

The question of the paper is: assuming that we are in the discrete case (x_i's are symmetric Bernoulli), how resilient is the Littlewood-Offord's anti-concentration result, i.e. how many of the x_i's an imaginary adversary typically allowed to change without being able to force concentration on a particular value? The authors give an asymptotic of the worst case resilience, and an (exact) lower bound on typical resilience. Speaker(s): Liza Rebrova (UM)