# On multiplicative Chung--Diaconis--Graham process

@inproceedings{Shkredov2021OnMC, title={On multiplicative Chung--Diaconis--Graham process}, author={I. Shkredov}, year={2021} }

We study the lazy Markov chain on Fp defined as Xn+1 = Xn with probability 1/2 and Xn+1 = f(Xn) · εn+1, where εn are random variables distributed uniformly on {γ, γ−1}, γ is a primitive root and f(x) = x x−1 or f(x) = ind(x). Then we show that the mixing time of Xn is exp(O(log p/ log log p)). Also, we obtain an application to an additive–combinatorial question concerning a certain Sidon–type family of sets.

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