Harmonicity and Invariance on the Slice
Harmonicity and Invariance on the Slice

Elchanan Mossel, University of Pennsylvania
Fine Hall 214
The subject of this talk is the slice of the discrete cube  i.e. the uniform distribution over all binary vector of a certain weight, or probabilistically the product measure on the cube conditioned on having a specific sum. I will review the L_2 theory of the slice as well as a the following new result: functions of low degree have similar distribution on the slice and the corresponding product measure on the cube. The proof relates harmonicity to decomposition of increasing path in terms of a Markov chain and a reverse Markov chain. Based on a joint work with Yuval Filmus (http://arxiv.org/abs/1507.02713).