Geodesic
Determinantal Expressions in Multi-Species TASEP
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height functions have a determinantal structure. In the homogeneous case and for certain initial conditions, the fluctuations of the height function converge to Gaussian random variables in the large-time limit. The proof utilizes a coupling between the multi-species TASEP and a coalescing random walk, and previously known results for coalescing random walks.
Keywords: determinantal, multi-species, coalescing.
Mots-clés : TASEP 
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     author = {Jeffrey Kuan},
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Jeffrey Kuan. Determinantal Expressions in Multi-Species TASEP. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a132/

[1] Assiotis T., “Random surface growth and Karlin–McGregor polynomials”, Electron. J. Probab., 23 (2018), 106, 81 pp., arXiv: 1709.10444 | DOI | MR | Zbl

[2] Baik J., Ferrari P. L., Péché S., “Limit process of stationary TASEP near the characteristic line”, Comm. Pure Appl. Math., 63 (2010), 1017–1070, arXiv: 0907.0226 | DOI | MR | Zbl

[3] Borodin A., Bufetov A., Leading particles in multi-type TASEP, in preparation

[4] Borodin A., Ferrari P. L., Prähofer M., “Fluctuations in the discrete TASEP with periodic initial configurations and the ${\rm Airy}_1$ process”, Int. Math. Res. Pap., 2007 (2007), rpm002, 47 pp., arXiv: math-ph/0611071 | DOI | MR | Zbl

[5] Borodin A., Ferrari P. L., Prähofer M., Sasamoto T., “Fluctuation properties of the TASEP with periodic initial configuration”, J. Stat. Phys., 129 (2007), 1055–1080, arXiv: math-ph/0608056 | DOI | MR | Zbl

[6] Borodin A., Ferrari P. L., Sasamoto T., “Large time asymptotics of growth models on space-like paths. II PNG and parallel TASEP”, Comm. Math. Phys., 283 (2008), 417–449, arXiv: 0707.4207 | DOI | MR | Zbl

[7] Borodin A., Ferrari P. L., Sasamoto T., “Transition between ${\rm Airy}_1$ and ${\rm Airy}_2$ processes and TASEP fluctuations”, Comm. Pure Appl. Math., 61 (2008), 1603–1629, arXiv: math-ph/0703023 | DOI | MR | Zbl

[8] Chatterjee S., Schütz G. M., “Determinant representation for some transition probabilities in the TASEP with second class particles”, J. Stat. Phys., 140 (2010), 900–916, arXiv: 1003.5815 | DOI | MR | Zbl

[9] Chen Z., de Gier J., Hiki I., Sasamoto T., “Exact confirmation of 1d nonlinear fluctuating hydrodynamics for a two-species exclusion process”, Phys. Rev. Lett., 120 (2018), 240601, 6 pp., arXiv: 1803.06829 | DOI

[10] Johansson K., “Discrete polynuclear growth and determinantal processes”, Comm. Math. Phys., 242 (2003), 277–329, arXiv: math.PR/0206208 | DOI | MR | Zbl

[11] Lee E., “On the TASEP with second class particles”, SIGMA, 14 (2018), 006, 17 pp., arXiv: 1705.10544 | DOI | MR | Zbl

[12] Quastel J., Remenik D., KP governs random growth of a one dimensional substrate, arXiv: 1908.10353

[13] Schütz G. M., “Exact solution of the master equation for the asymmetric exclusion process”, J. Stat. Phys., 88 (1997), 427–445, arXiv: cond-mat/9701019 | DOI | Zbl

[14] Warren J., “Dyson's Brownian motions, intertwining and interlacing”, Electron. J. Probab., 12:19 (2007), 573–590, arXiv: math.PR/0509720 | DOI | MR | Zbl