We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by @math , which creates a shock in the particle density of order @math @math the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit @math one recovers the product limit law and the degeneration of the correlation length observed at shocks of order @math . This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several @math processes.
Here we rehash some of the known results that we will use in this paper, and describe the method of proof from @cite_20 , which is relevant to this paper.
@cite_20
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A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results.