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).