--- res: bibo_abstract: - 'Consider the sum X(ξ)=∑ni=1aiξi , where a=(ai)ni=1 is a sequence of non-zero reals and ξ=(ξi)ni=1 is a sequence of i.i.d. Rademacher random variables (that is, Pr[ξi=1]=Pr[ξi=−1]=1/2 ). The classical Littlewood-Offord problem asks for the best possible upper bound on the concentration probabilities Pr[X=x] . In this paper we study a resilience version of the Littlewood-Offord problem: how many of the ξi is an adversary typically allowed to change without being able to force concentration on a particular value? We solve this problem asymptotically, and present a few interesting open problems.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Afonso S. foaf_name: Bandeira, Afonso S. foaf_surname: Bandeira - foaf_Person: foaf_givenName: Asaf foaf_name: Ferber, Asaf foaf_surname: Ferber - foaf_Person: foaf_givenName: Matthew Alan foaf_name: Kwan, Matthew Alan foaf_surname: Kwan foaf_workInfoHomepage: http://www.librecat.org/personId=5fca0887-a1db-11eb-95d1-ca9d5e0453b3 orcid: 0000-0002-4003-7567 bibo_doi: 10.1016/j.aim.2017.08.031 bibo_volume: 319 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0001-8708 dct_language: eng dct_publisher: Elsevier@ dct_title: Resilience for the Littlewood–Offord problem@ ...