Electronic Communications in Probability

Microscopic structure of a decreasing shock for the asymmetric $k$-step exclusion process

Herve Guiol, Krishnamurthi Ravishankar, and Ellen Saada

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Abstract

The asymmetric $k$-step exclusion processes are the simplest interacting particle systems whose hydrodynamic equation may exhibit both increasing and decreasing entropic shocks under Euler scaling. We prove that, under Riemann initial condition with right density zero and adequate left density, the rightmost particle identifies microscopically the decreasing shock.

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 19, 170-178.

Dates
Accepted: 22 December 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608903

Digital Object Identifier
doi:10.1214/ECP.v8-1080

Mathematical Reviews number (MathSciNet)
MR2042756

Zentralblatt MATH identifier
1067.82048

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Asymmetric k-step exclusion process Non-convex or non-concave flux microscopic shock rightmost particle

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Guiol, Herve; Ravishankar, Krishnamurthi; Saada, Ellen. Microscopic structure of a decreasing shock for the asymmetric $k$-step exclusion process. Electron. Commun. Probab. 8 (2003), paper no. 19, 170--178. doi:10.1214/ECP.v8-1080. https://projecteuclid.org/euclid.ecp/1463608903


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References

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