Lecture 17 Lecturer : Anna Karlin Scribe : Eric

نویسنده

  • Anna Karlin
چکیده

Coupling is a useful tool in the analysis of the mixing time of Markov chains. The basic idea is that a Markov chain that is initialized to some arbitrary distribution can be compared via coupling with another Markov chain that is initialized to the stationary distribution. The two chains then progress simultaneously, and the distance between the two chains at any time indicates how close the randomly initialized distribution is to the stationary distribution. The total variation distance between two distributions D1 and D2 on the same sample space Ω is defined as

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تاریخ انتشار 2013