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Mathematical and General}, VOLUME = {38}, YEAR = {2005}, NUMBER = {19}, PAGES = {R195}, ISSN = {0305-4470}, CODEN = {JPHAC5}, MRCLASS = {82C20 (82-02)}, MRNUMBER = {2145800 (2005m:82099)}, DOI = {10.1088/0305-4470/38/19/R01}, URL = {http://dx.doi.org/10.1088/0305-4470/38/19/R01}, } @article{prolhac-evans-mallick-2009, author={Sylvain Prolhac and Martin R. Evans and Kirone Mallick}, title={The matrix product solution of the multispecies partially asymmetric exclusion process}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical}, volume={42}, number={16}, pages={165004}, url={http://stacks.iop.org/1751-8121/42/i=16/a=165004}, year={2009} } @Article{evans-ferrari-mallick-2009, author="Evans, Martin R. and Ferrari, Pablo A. and Mallick, Kirone", title="Matrix Representation of the Stationary Measure for the Multispecies {TASEP}", journal="Journal of Statistical Physics", year="2009", volume="135", number="2", pages="217--239", abstract="In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N>2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.", issn="1572-9613", doi="10.1007/s10955-009-9696-2", url="https://doi.org/10.1007/s10955-009-9696-2" } @article {ayyer-linusson-2014, AUTHOR = {Ayyer, Arvind and Linusson, Svante}, TITLE = {An inhomogeneous multispecies {TASEP} on a ring}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {57}, YEAR = {2014}, PAGES = {21--43}, ISSN = {0196-8858}, MRCLASS = {60K35 (05A05)}, MRNUMBER = {3206520}, MRREVIEWER = {Halim Zeghdoudi}, DOI = {10.1016/j.aam.2014.02.001}, URL = {http://dx.doi.org/10.1016/j.aam.2014.02.001}, } @article {arita-mallick-2013, AUTHOR = {Arita, Chikashi and Mallick, Kirone}, TITLE = {Matrix product solution of an inhomogeneous multi-species {TASEP}}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical}, VOLUME = {46}, YEAR = {2013}, NUMBER = {8}, PAGES = {085002, 11}, ISSN = {1751-8113}, MRCLASS = {81S22 (15A72 60K35)}, MRNUMBER = {3030185}, MRREVIEWER = {George M. Tsaklidis}, DOI = {10.1088/1751-8113/46/8/085002}, URL = {http://dx.doi.org/10.1088/1751-8113/46/8/085002}, } @article{ayyer-linusson-2016, AUTHOR = {Ayyer, Arvind and Linusson, Svante}, TITLE = {Correlations in the multispecies {TASEP} and a conjecture by {L}am}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {369}, YEAR = {2017}, NUMBER = {2}, PAGES = {1097--1125}, ISSN = {0002-9947}, MRCLASS = {60K35 (05A05 05A17 20F55)}, MRNUMBER = {3572266}, DOI = {10.1090/tran/6806}, URL = {https://doi.org/10.1090/tran/6806}, } @article {amir-angel-valko-2011, AUTHOR = {Amir, Gideon and Angel, Omer and Valk\'o, Benedek}, TITLE = {The {TASEP} speed process}, JOURNAL = {Ann. 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