--- _id: '9588' abstract: - lang: eng text: '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.' article_processing_charge: No article_type: original author: - first_name: Afonso S. full_name: Bandeira, Afonso S. last_name: Bandeira - first_name: Asaf full_name: Ferber, Asaf last_name: Ferber - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 citation: ama: Bandeira AS, Ferber A, Kwan MA. Resilience for the Littlewood–Offord problem. Advances in Mathematics. 2017;319:292-312. doi:10.1016/j.aim.2017.08.031 apa: Bandeira, A. S., Ferber, A., & Kwan, M. A. (2017). Resilience for the Littlewood–Offord problem. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2017.08.031 chicago: Bandeira, Afonso S., Asaf Ferber, and Matthew Alan Kwan. “Resilience for the Littlewood–Offord Problem.” Advances in Mathematics. Elsevier, 2017. https://doi.org/10.1016/j.aim.2017.08.031. ieee: A. S. Bandeira, A. Ferber, and M. A. Kwan, “Resilience for the Littlewood–Offord problem,” Advances in Mathematics, vol. 319. Elsevier, pp. 292–312, 2017. ista: Bandeira AS, Ferber A, Kwan MA. 2017. Resilience for the Littlewood–Offord problem. Advances in Mathematics. 319, 292–312. mla: Bandeira, Afonso S., et al. “Resilience for the Littlewood–Offord Problem.” Advances in Mathematics, vol. 319, Elsevier, 2017, pp. 292–312, doi:10.1016/j.aim.2017.08.031. short: A.S. Bandeira, A. Ferber, M.A. Kwan, Advances in Mathematics 319 (2017) 292–312. date_created: 2021-06-22T11:51:27Z date_published: 2017-10-15T00:00:00Z date_updated: 2023-02-23T14:01:57Z day: '15' doi: 10.1016/j.aim.2017.08.031 extern: '1' external_id: arxiv: - '1609.08136' intvolume: ' 319' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1609.08136 month: '10' oa: 1 oa_version: Preprint page: 292-312 publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Resilience for the Littlewood–Offord problem type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 319 year: '2017' ...