IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i4p1165-1207.html
   My bibliography  Save this article

Self-duality and shock dynamics in the n-species priority ASEP

Author

Listed:
  • Belitsky, V.
  • Schütz, G.M.

Abstract

We construct all invariant measures of the n-species priority asymmetric simple exclusion process with reflecting boundaries and prove reversibility. Using the symmetry of the generator of the process under the quantum algebra Uq[gl(n+1)] we derive self-duality functions. From these we obtain in explicit form the time evolution on Z of a family of measures with K shocks in terms of the transition probability of a shock exclusion process with K coloured particles with particle-dependent hopping rates and nearest-neighbour colour exchange. This process is a gas of particles that form a bound state, corresponding to shock coalescence on macroscopic scale.

Suggested Citation

  • Belitsky, V. & Schütz, G.M., 2018. "Self-duality and shock dynamics in the n-species priority ASEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1165-1207.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1165-1207
    DOI: 10.1016/j.spa.2017.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917301710
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.07.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Carinci, Gioia & Giardinà, Cristian & Giberti, Claudio & Redig, Frank, 2015. "Dualities in population genetics: A fresh look with new dualities," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 941-969.
    2. Lloyd, Peter & Sudbury, Aidan & Donnelly, Peter, 1996. "Quantum operators in classical probability theory: I. "Quantum spin" techniques and the exclusion model of diffusion," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 205-221, February.
    3. Benjamini, I. & Ferrari, P. A. & Landim, C., 1996. "Asymmetric conservative processes with random rates," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 181-204, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beltrán, Johel, 2005. "Regularity of diffusion coefficient for nearest neighbor asymmetric simple exclusion on," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1451-1474, September.
    2. Gielis, G. & Koukkous, A. & Landim, C., 1998. "Equilibrium fluctuations for zero range processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 187-205, September.
    3. Andjel, E. D. & Ferrari, P. A. & Guiol, H. & Landim *, C., 2000. "Convergence to the maximal invariant measure for a zero-range process with random rates," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 67-81, November.
    4. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.
    5. Großkinsky, Stefan, 2008. "Equivalence of ensembles for two-species zero-range invariant measures," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1322-1350, August.
    6. Frank Hollander & Shubhamoy Nandan, 2022. "Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1795-1841, September.
    7. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.
    8. Kon Kam King, Guillaume & Pandolfi, Andrea & Piretto, Marco & Ruggiero, Matteo, 2024. "Approximate filtering via discrete dual processes," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    9. Koukkous, A., 1999. "Hydrodynamic behavior of symmetric zero-range processes with random rates," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 297-312, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1165-1207. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.