1
Applications of Jensen’s inequality
2
Shannon entropy inequalities
3
Entropic Ruzsa calculus
4
The 100% version of PFR
5
The Fibring lemma
6
Entropy version of PFR
▶
6.1
Basic facts about minimizers
6.2
First estimate
6.3
Second estimate
6.4
Endgame
6.5
Conclusion
7
Proof of PFR
8
Improving the exponents
9
Homomorphism version of PFR
10
Approximate homomorphism version of PFR
11
Weak PFR over the integers
12
The \(m\)-torsion case
▶
12.1
Data processing inequality
12.2
More Ruzsa distance estimates
12.3
Multidistance
12.4
The tau functional
12.5
The multidistance chain rule
12.6
Bounding the mutual information
12.7
Endgame
12.8
Wrapping up
13
Further improvement to exponent
▶
13.1
Kullback–Leibler divergence
13.2
Rho functionals
13.3
Studying a minimizer
Dependency graph
PFR
1
Applications of Jensen’s inequality
2
Shannon entropy inequalities
3
Entropic Ruzsa calculus
4
The 100% version of PFR
5
The Fibring lemma
6
Entropy version of PFR
6.1
Basic facts about minimizers
6.2
First estimate
6.3
Second estimate
6.4
Endgame
6.5
Conclusion
7
Proof of PFR
8
Improving the exponents
9
Homomorphism version of PFR
10
Approximate homomorphism version of PFR
11
Weak PFR over the integers
12
The \(m\)-torsion case
12.1
Data processing inequality
12.2
More Ruzsa distance estimates
12.3
Multidistance
12.4
The tau functional
12.5
The multidistance chain rule
12.6
Bounding the mutual information
12.7
Endgame
12.8
Wrapping up
13
Further improvement to exponent
13.1
Kullback–Leibler divergence
13.2
Rho functionals
13.3
Studying a minimizer