{"external_id":{"arxiv":["1609.08136"]},"language":[{"iso":"eng"}],"page":"93-99","publication":"Electronic Notes in Discrete Mathematics","_id":"9574","day":"01","status":"public","date_created":"2021-06-21T06:31:10Z","scopus_import":"1","publication_identifier":{"issn":["1571-0653"]},"month":"08","date_published":"2017-08-01T00:00:00Z","article_processing_charge":"No","publication_status":"published","publisher":"Elsevier","author":[{"full_name":"Bandeira, Afonso S.","first_name":"Afonso S.","last_name":"Bandeira"},{"first_name":"Asaf","full_name":"Ferber, Asaf","last_name":"Ferber"},{"orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","last_name":"Kwan"}],"oa_version":"Preprint","article_type":"original","extern":"1","intvolume":"        61","title":"Resilience for the Littlewood-Offord problem","type":"journal_article","citation":{"mla":"Bandeira, Afonso S., et al. “Resilience for the Littlewood-Offord Problem.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 61, Elsevier, 2017, pp. 93–99, doi:<a href=\"https://doi.org/10.1016/j.endm.2017.06.025\">10.1016/j.endm.2017.06.025</a>.","chicago":"Bandeira, Afonso S., Asaf Ferber, and Matthew Alan Kwan. “Resilience for the Littlewood-Offord Problem.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.endm.2017.06.025\">https://doi.org/10.1016/j.endm.2017.06.025</a>.","short":"A.S. Bandeira, A. Ferber, M.A. Kwan, Electronic Notes in Discrete Mathematics 61 (2017) 93–99.","ista":"Bandeira AS, Ferber A, Kwan MA. 2017. Resilience for the Littlewood-Offord problem. Electronic Notes in Discrete Mathematics. 61, 93–99.","apa":"Bandeira, A. S., Ferber, A., &#38; Kwan, M. A. (2017). Resilience for the Littlewood-Offord problem. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2017.06.025\">https://doi.org/10.1016/j.endm.2017.06.025</a>","ieee":"A. S. Bandeira, A. Ferber, and M. A. Kwan, “Resilience for the Littlewood-Offord problem,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 61. Elsevier, pp. 93–99, 2017.","ama":"Bandeira AS, Ferber A, Kwan MA. Resilience for the Littlewood-Offord problem. <i>Electronic Notes in Discrete Mathematics</i>. 2017;61:93-99. doi:<a href=\"https://doi.org/10.1016/j.endm.2017.06.025\">10.1016/j.endm.2017.06.025</a>"},"doi":"10.1016/j.endm.2017.06.025","date_updated":"2023-02-23T14:01:26Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1609.08136"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","volume":61,"oa":1,"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"}],"quality_controlled":"1","year":"2017"}