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Transfer matrices for the totally asymmetric simple exclusion process

Abstract : We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L−1,L}$ and $\tilde T_{L−1,L}$ that intertwine the Markov matrices of consecutive system sizes:$\tilde T_{L−1,L}$$M_{L−1} = M_LT_{L−1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.
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Marko Woelki, Kirone Mallick. Transfer matrices for the totally asymmetric simple exclusion process. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (18), pp.185003. ⟨10.1088/1751-8113/43/18/185003⟩. ⟨cea-02924648⟩

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