Entropic Ruzsa calculus

In this section \(G\) will be a finite additive group. (May eventually want to generalize to infinite \(G\).)

Negation preserves entropy to Alternate form of distance

• Negation preserves entropy
• Shearing preserves entropy
• Lower bound of sumset
• Conditional lower bound on sumset
• Independent lower bound on sumset
• Copy preserves entropy
• Existence of independent copies
• Ruzsa distance
• Distance from zero
• Copy preserves Ruzsa distance
• Ruzsa distance in independent case
• Distance symmetric
• Distance controls entropy difference
• Distance controls entropy growth
• Distance nonnegative
• Projection entropy and distance
• Improved Ruzsa triangle inequality
• Ruzsa triangle inequality
• Conditioned Ruzsa distance
• Alternate form of distance

Kaimanovich-Vershik-Madiman… to Comparison of Ruzsa distances…

• Kaimanovich-Vershik-Madiman inequality
• Existence of conditional independent trials
• Balog-Szemerédi-Gowers
• Upper bound on conditioned Ruzsa distance
• Comparison of Ruzsa distances, I
• Comparison of Ruzsa distances, II

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