· 2016· Preprint
NONLINEAR LARGE DEVIATIONS
- 121citations
- 2016year
Short summary
A new technique computes large deviations for nonlinear functions of Bernoulli variables, enabling analysis of subgraph counts in sparse random graphs where prior methods failed.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces a general technique for computing large deviations of nonlinear functions of Bernoulli random variables.
- Applies the method to calculate large deviation rate functions for subgraph counts in sparse random graphs.
- Extends analysis to exponential random graphs and three-term arithmetic progressions in random integer sets.
- Overcomes limitations of prior methods that were restricted to dense graphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
We present a general technique for computing large deviations of nonlinear functions of independent Bernoulli random variables. The method is applied to compute the large deviation rate functions for subgraph counts in sparse random graphs. Previous technology, based on Szemerédi's regularity lemma, works only for dense graphs. Applications are also made to exponential random graphs and three-term arithmetic progressions in random sets of integers.
The authors' abstract, as published at the source., 2016 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics