Geodesic
The~Kardar--Parisi--Zhang equation and its matrix generalization
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 416-432

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We study the problem of the condensate (stochastic average) origination for an auxiliary field in the Kardar–Parisi–Zhang equation and its matrix generalization. We cannot reliably conclude that there is a condensate for the Kardar–Parisi–Zhang equation in the framework of the one-loop approximation improved by the renormalization group method. The matrix generalization of the Kardar–Parisi–Zhang equation permits a positive answer to the question of whether there is a nonzero condensate, and the problem can be solved exactly in the large-$N$ limit.
Keywords: Kardar–Parisi–Zhang equation, renormalization group, effective potential, $1/N$-expansion. 
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     title = {The~Kardar--Parisi--Zhang equation and its matrix generalization},
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L. V. Bork; S. L. Ogarkov. The~Kardar--Parisi--Zhang equation and its matrix generalization. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 416-432. http://geodesic.mathdoc.fr/item/TMF_2014_178_3_a6/