{"year":"2017","abstract":[{"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.","lang":"eng"}],"title":"Resilience for the Littlewood–Offord problem","_id":"9588","article_type":"original","month":"10","oa_version":"Preprint","doi":"10.1016/j.aim.2017.08.031","status":"public","publication":"Advances in Mathematics","page":"292-312","publisher":"Elsevier","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","citation":{"chicago":"Bandeira, Afonso S., Asaf Ferber, and Matthew Alan Kwan. “Resilience for the Littlewood–Offord Problem.” <i>Advances in Mathematics</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">https://doi.org/10.1016/j.aim.2017.08.031</a>.","short":"A.S. Bandeira, A. Ferber, M.A. Kwan, Advances in Mathematics 319 (2017) 292–312.","mla":"Bandeira, Afonso S., et al. “Resilience for the Littlewood–Offord Problem.” <i>Advances in Mathematics</i>, vol. 319, Elsevier, 2017, pp. 292–312, doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">10.1016/j.aim.2017.08.031</a>.","ista":"Bandeira AS, Ferber A, Kwan MA. 2017. Resilience for the Littlewood–Offord problem. Advances in Mathematics. 319, 292–312.","ieee":"A. S. Bandeira, A. Ferber, and M. A. Kwan, “Resilience for the Littlewood–Offord problem,” <i>Advances in Mathematics</i>, vol. 319. Elsevier, pp. 292–312, 2017.","apa":"Bandeira, A. S., Ferber, A., &#38; Kwan, M. A. (2017). Resilience for the Littlewood–Offord problem. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">https://doi.org/10.1016/j.aim.2017.08.031</a>","ama":"Bandeira AS, Ferber A, Kwan MA. Resilience for the Littlewood–Offord problem. <i>Advances in Mathematics</i>. 2017;319:292-312. doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">10.1016/j.aim.2017.08.031</a>"},"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1609.08136","open_access":"1"}],"volume":319,"date_published":"2017-10-15T00:00:00Z","date_updated":"2023-02-23T14:01:57Z","publication_identifier":{"issn":["0001-8708"]},"author":[{"last_name":"Bandeira","first_name":"Afonso S.","full_name":"Bandeira, Afonso S."},{"first_name":"Asaf","full_name":"Ferber, Asaf","last_name":"Ferber"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","last_name":"Kwan"}],"date_created":"2021-06-22T11:51:27Z","oa":1,"type":"journal_article","quality_controlled":"1","scopus_import":"1","day":"15","external_id":{"arxiv":["1609.08136"]},"extern":"1","article_processing_charge":"No","intvolume":"       319"}