2021
DOI: 10.4310/joc.2021.v12.n1.a6
|View full text |Cite
|
Sign up to set email alerts
|

Threshold functions for substructures in random subsets of finite vector spaces

Abstract: The study of substructures in random objects has a long history, beginning with Erdős and Rényi's work on subgraphs of random graphs. We study the existence of certain substructures in random subsets of vector spaces over finite fields. First we provide a general framework which can be applied to establish coarse threshold results and prove a limiting Poisson distribution at the threshold scale. To illustrate our framework we apply our results to k-term arithmetic progressions, sums, right triangles, parallelo… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
3
0

Year Published

2022
2022
2022
2022

Publication Types

Select...
1

Relationship

0
1

Authors

Journals

citations
Cited by 1 publication
(3 citation statements)
references
References 33 publications
0
3
0
Order By: Relevance
“…Theorem 1.1 (Chen-Greenhill, [4]). Let F be a family of ℓ-subsets of F n q , and X be a random subset chosen as above.…”
Section: Pr[γ] → 1 If θ = ω(T)mentioning
confidence: 99%
See 2 more Smart Citations
“…Theorem 1.1 (Chen-Greenhill, [4]). Let F be a family of ℓ-subsets of F n q , and X be a random subset chosen as above.…”
Section: Pr[γ] → 1 If θ = ω(T)mentioning
confidence: 99%
“…As consequences, they obtained threshold functions for several precise geometric structures; for examples, non-trivial k-term arithmetic progressions, non-trivial parallelograms, and non-trivial right angles. We refer the interested reader to [4] for more details.…”
Section: Pr[γ] → 1 If θ = ω(T)mentioning
confidence: 99%
See 1 more Smart Citation