On the sum of the L 1 influences of bounded functions

Research output: Contribution to journalArticlepeer-review


Let f: {-1, 1}n → [-1, 1] have degree d as a multilinear polynomial. It is well-known that the total influence of f is at most d. Aaronson and Ambainis asked whether the total L1 influence of f can also be bounded as a function of d. Bačkurs and Bavarian answered this question in the affirmative, providing a bound of O(d3) for general functions and O(d2) for homogeneous functions. We improve on their results by providing a bound of d2 for general functions and O(d log d) for homogeneous functions. In addition, we prove a bound of d/(2p) + o(d) for monotone functions, and provide a matching example.

Original languageEnglish
Pages (from-to)167-192
Number of pages26
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Jul 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'On the sum of the L 1 influences of bounded functions'. Together they form a unique fingerprint.

Cite this