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A spectral method for identifying lumping in large Markov chains ispresented. Identification of meta stable states is treated as a special case.The method is based on spectral analysis of a self-adjoint matrix that is afunction of the original transition matrix. It is demonstrated that thetechnique is more robust than existing methods when applied to noisynon-reversible Markov chains.

A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains