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