One-arm extension estimate

The Russo-Seymour-Welsh theorem and the Harris-FKG inequality imply

π (2 r) \geq c π (r)

for a scale-independent constant

c > 0

.

Table of contents
- RSW gluing lemma for two one-arm events One-arm extension estimate

RSW gluing lemma for two one-arm events

RSW rectangle crossings and positive association join two separated one-arm events with probability bounded below uniformly over scale.

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 212 / 1 / b / Solution

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