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The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhanguniversality class using the techniques from random matrix theory are reviewedfrom the point of view of the asymmetric simple exclusion process. We explainthe basics of random matrix techniques, the connections to the polynucleargrowth models and a method using the Green's function.

Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques