Mixing time of fractional random walk on finite fields

We study a random walk on Fp defined by Xn+1=1∕Xn+εn+1 if Xn≠0, and Xn+1=εn+1 Xn=0, where εn+1 are independent identically distributed. This can be seen as non-linear analogue of the Chung–Diaconis–Graham process. show that mixing time is order logp, answering question Chatterjee Diaconis.