Nonlinear large deviations
Copyright policy )Nonlinear large deviations
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 Szemeredi'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.
43 pages. To appear in Adv. Math
- New York University United States
- Stanford University United States
Erdős-Rényi random graph, Combinatorial probability, exponential random graph models, Probability (math.PR), Random graphs (graph-theoretic aspects), 60F10, 05C80, 60C05, 05A20, Combinatorial inequalities, concentration of measure, arithmetic progressions, Large deviations, regularity lemma, sparse random graphs, FOS: Mathematics, Inequalities; stochastic orderings, Mathematics - Combinatorics, Probability distributions: general theory, nonlinear large deviations, Combinatorics (math.CO), Mathematics - Probability
Erdős-Rényi random graph, Combinatorial probability, exponential random graph models, Probability (math.PR), Random graphs (graph-theoretic aspects), 60F10, 05C80, 60C05, 05A20, Combinatorial inequalities, concentration of measure, arithmetic progressions, Large deviations, regularity lemma, sparse random graphs, FOS: Mathematics, Inequalities; stochastic orderings, Mathematics - Combinatorics, Probability distributions: general theory, nonlinear large deviations, Combinatorics (math.CO), Mathematics - Probability
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