On Thouvenot's ergodic proof of Roth's theorem

We present a lecture note on Thouvenot's proof of the Roth-Furstenberg theorem and joining proofs of Furstenberg's theorems on multiple progression average mixing for weakly mixing transformations.Comment: lecture note

Simple Spectrum for Tensor Products of Mixing Map Powers

We prove the existence of a mixing rank one map $T$ such that the product $T\otimes T^2\otimes T^3\otimes...$ has simple spectrum. This result is used in S.V. Thikhonov's proof of the existence of mixing transformation with homogeneous spectrum of multiplicity $m>2$.Comment: 7 page