---
res:
  bibo_abstract:
  - "Consider a quadratic polynomial Q(ξ1, . . . , ξn) of independent Rademacher random
    variables ξ1, . . . , ξn. To what extent can Q(ξ1, . . . , ξn) concentrate on
    a single value? This quadratic version of the classical Littlewood–Offord problem
    was popularised by Costello, Tao and Vu in their study of symmetric random matrices.
    In this paper, we obtain an essentially optimal bound for this problem, as conjectured
    by Nguyen and Vu. Specifically, if Q(ξ1, . . . , ξn) ‘robustly depends on at least
    m of the ξi’ in the sense that there is no way to pin down the value of Q(ξ1,
    . . . , ξn) by fixing values for fewer than m of the variables ξi, then we have
    Pr[Q(ξ1, . . . , ξn) = 0] ≤ O(1/√m). This also implies a similar result in the
    case where ξ1, . . . , ξn have arbitrary distributions. Our proof combines a number
    of ideas that may be of independent interest, including an inductive decoupling
    scheme that reduces quadratic anticoncentration problems\r\nto high-dimensional
    linear anticoncentration problems. Also, one application of our main result is
    the resolution of a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn related
    to graph inducibility. @eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Matthew Alan
      foaf_name: Kwan, Matthew Alan
      foaf_surname: Kwan
      foaf_workInfoHomepage: http://www.librecat.org/personId=5fca0887-a1db-11eb-95d1-ca9d5e0453b3
    orcid: 0000-0002-4003-7567
  - foaf_Person:
      foaf_givenName: Lisa
      foaf_name: Sauermann, Lisa
      foaf_surname: Sauermann
  bibo_doi: 10.1112/S0010437X25102789
  bibo_issue: '12'
  bibo_volume: 161
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0010-437X
  - http://id.crossref.org/issn/1570-5846
  dct_language: eng
  dct_publisher: Cambridge University Press@
  dct_title: Resolution of the quadratic Littlewood–Offord problem@
...