Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes
Hydrodynamical limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes
复制标题
空间非均匀一维完全不对称零程过程的流体动力学极限
DOI：
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发表时间：
1996
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影响因子：
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通讯作者：
C. Landim
中科院分区：
文献类型：
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作者：
C. Landim
我们考虑z上跳跃率有界的完全不对称吸引零距离过程。为了得到与经验测度的水动力极限有较大偏差的下界，我们用两种方法对过程进行扰动。我们首先选择有限数量的位点，减慢这些位点的跳跃速率。我们证明了这个扰动过程的一个流体动力学极限，并在速率减慢的地方显示了狄拉克测度的出现。第二类扰动包括选择有限数量的粒子，并使它们以较慢的速度跳跃。在这些情况下，流体动力极限用拟线性一阶双曲方程的非熵弱解来描述。这两个结果证明了跳跃率有界的非对称过程的大偏差至少为e- CN数量级。所有这些结果都可以转化为完全不对称的简单不相容过程，其中有限数量的粒子或有限数量的空穴以较慢的速率跳跃。
We consider totally asymmetric attractive zero-range processes with bounded jump rates on Z. In order to obtain a lower bound for the large deviations from the hydrodynamical limit of the empirical measure, we perturb the process in two ways. We first choose a finite number of sites and slow down the jump rate at these sites. We prove a hydrodynamical limit for this perturbed process and show the appearance of Dirac measures on the sites where the rates are slowed down. The second type of perturbation consists of choosing a finite number of particles and making them jump at a slower rate. In these cases the hydrodynamical limit is described by nonentropy weak solutions of quasilinear first-order hyperbolic equations. These two results prove that the large deviations for asymmetric processes with bounded jump rates are of order at least e- CN . All these results can be translated to the context of totally asymmetric simple exclusion processes where a finite number of particles or a finite number of holes jump at a slower rate.