I will discuss the noise sensitivity of Boolean functions on the symmetric group, where the noise is generated by a Markov chain on the symmetric group. The main focus will be on comparison results between different noise sources and their applications. I will present several examples, including the result that the indicator of long cycles is noise-sensitive under the interchange process on the discrete torus in any fixed dimension.
This talk is based on recent joint work with Gideon Amir (arXiv: [ 2606_29829 ]
