 98159 Derrida B., Goldstein S., Lebowitz J.L., Speer E.
 Shift Equivalence of Measures and the Intrinsic Structure of
Shocks in the Asymmetric Simple Exclusion Process
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Mar 6, 98

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Abstract. We investigate properties of nontranslationinvariant measures, describing
particle systems on $\bbz$, which are asymptotic to different translation
invariant measures on the left and on the right. Often the structure of
the transition region can only be observed from a point of view which is
randomin particular, configuration dependent. Two such measures will be
called {\it shift equivalent} if they differ only by the choice of such a
viewpoint. We introduce certain quantities, called {\it translation sums},
which, under some auxiliary conditions, characterize the equivalence
classes. Our prime example is the asymmetric simple exclusion process, for
which the measures in question describe the microscopic structure of
shocks. In this case we compute explicitly the translation sums and find
that shocks generated in different waysin particular, via initial
conditions in an infinite system or by boundary conditions in a finite
systemare described by shift equivalent measures. We show also that
when the shock in the infinite system is observed from the location of a
second class particle, treating this particle either as a first class
particle or as an empty site leads to shift equivalent shock measures.
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