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