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Second Class Particles as Microscopic Characteristics in Totally Asymmetric Nearest-Neighbor K-Exclusion Processes

Timo Seppäläinen
Transactions of the American Mathematical Society
Vol. 353, No. 12 (Dec., 2001), pp. 4801-4829
Stable URL: http://www.jstor.org/stable/2693906
Page Count: 29
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Second Class Particles as Microscopic Characteristics in Totally Asymmetric Nearest-Neighbor K-Exclusion Processes
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Abstract

We prove laws of large numbers for a second class particle in one-dimensional totally asymmetric K-exclusion processes, under hydrodynamic Euler scaling. The assumption required is that initially the ambient particle configuration converges to a limiting profile. The macroscopic trajectories of second class particles are characteristics and shocks of the conservation law of the particle density. The proof uses a variational representation of a second class particle, to overcome the problem of lack of information about invariant distributions. But we cannot rule out the possibility that the flux function of the conservation law may be neither differentiable nor strictly concave. To give a complete picture we discuss the construction, uniqueness, and other properties of the weak solution that the particle density obeys.

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