# CSM

## Seminar

### Path coupling without contraction

Seminar Room 1, Newton Institute

#### Abstract

Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than defining and analysing the coupling on every pair in the state space of the Markov chain, analysis is done on a smaller set S. If the coefficient of contraction b is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if b=1 then analysis (of the variance) is still required for all pairs in the state space. In this paper we present a new approach which shows rapid mixing in the case b=1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved.

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