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CROSSING PROBABILITIES
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Homological Percolation: The Formation of Giant Cycles
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- 1 Intro
- 2 PERSISTENT HOMOLOGY
- 3 THE MAXIMAL PERSISTENCE OF NOISE
- 4 TYPICAL BEHAVIOR
- 5 CROSSING PROBABILITIES
- 6 CONT. PERC. IN A BOX - SETUP
- 7 CONT. PERC. - GIANT COMPONENTS
- 8 "GIANT" K-CYCLES
- 9 HOMOLOGICAL PERCOLATION
- 10 MAIN RESULT
- 11 SIGNAL VS. NOISE
- 12 H, PERCOLATION
- 13 DUALITY - PROOF
- 14 H.- -PERCOLATION
- 15 BIG PICTURE?
- 16 EULER CHARACTERISTIC
- 17 EC & PERCOLATION?
- 18 SIMULATIONS
- 19 PERMUTAHEDRAL SITE-PERCOLATION
- 20 GAUSSIAN RANDOM FIELDS
- 21 SUMMARY & FUTURE WORK
