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