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Exclusion processes and boundary conditions. (English) Zbl 1117.82017

Summary: A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter solvable family of pushing processes with certain rates on the continuum [M. Alimohammadi, V. Karimipour and M. Khorrami, Phys, Rev. E 57, 63–70 (1998), J. Stat. Phys. 97, No. 1–2, 373–394 (1999; Zbl 1006.82020), F. Roshani and M. Khorrami, Phys. Rev. E 60, 3393 (1999)]. The conditional probabilities are calculated using the Bethe ansatz, and it is shown that at large times they behave like the corresponding conditional probabilities of the family of diffusion-pushing processes introduced in the cited references.

MSC:

82B23 Exactly solvable models; Bethe ansatz
35Q53 KdV equations (Korteweg-de Vries equations)

Citations:

Zbl 1006.82020
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References:

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