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