an:01453267
Zbl 0971.60099
Ferrari, P. A.; Fontes, L. R. G.; Vares, M. E.
The asymmetric simple exclusion model with multiple shocks
EN
Ann. Inst. Henri Poincar??, Probab. Stat. 36, No. 2, 109-126 (2000).
00064343
2000
j
60K35 82C22 82C24
asymmetric simple exclusion process; dynamical phase transition; shock fluctuations
The paper deals with the PDE \(\partial_{t}\rho+\gamma\partial_{r}(\rho(1-\rho))=0\) which describes the hydrodynamical behaviour of the one-dimensional asymmetric exclusion process and where \(\gamma\) is the mean of the jump distribution. The problem which is more especially considered here is the description of the microscopic behaviour of the system at certain discontinuity points (or shock fronts) of the solution of this equation, when the initial distribution has shocks (discontinuities). It is shown that the density converges weakly to a random measure with piecewise constant density while the points of discontinuity depend on these limiting Gaussian variables.
Guy Jumarie (Montr??al)