Contents

1. Introduction  
1.1. The ordinary percolation model  
1.2. The dynamical percolation model  
1.3. Outline of paper  

2. Dynamical percolation: first results  
2.1. Away from criticality  
2.2. Graphs with exceptional times exist  
2.3. High dimensional Euclidean case  

3. Exceptional times of percolation: the tree case

4. Noise sensitivity, noise stability, influence and the Fourier spectrum  
4.1. Definition of noise sensitivity, noise stability and some examples  
4.2. The noise sensitivity exponent, the noise stability exponent, and influence  
4.3. The Fourier spectrum  

5. Critical exponents for percolation

6. Exceptional times and positivity of the noise sensitivity exponent for the hexagonal lattice

7. The exact Hausdorff dimension of exceptional times and the exact noise sensitivity exponent for the hexagonal lattice

8. Sensitivity of the infinite cluster in critical percolation

9. Dynamical percolation and the incipient infinite cluster  
9.1. The incipient infinite cluster  
9.2. The incipient infinite cluster and dynamical percolation  

10. The scaling limit of planar dynamical percolation

11. Dynamical percolation for interacting particle systems