WIAS Preprint No. 1346, (2008)

Slow decorrelations in KPZ growth


  • Ferrari, Patrik

2010 Mathematics Subject Classification

  • 82C22 60K35


  • KPZ class, correlations, Airy processes


For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in $1+1$ dimensions, fluctuations grow as $t^1/3$ during time $t$ and the correlation length at a fixed time scales as $t^2/3$. In this note we discuss the scale of time correlations. For a representant of the KPZ class, the polynuclear growth model, we show that the space-time is non-trivially fibred, having slow directions with decorrelation exponent equal to $1$ instead of the usual $2/3$. These directions are the characteristic curves of the PDE associated to the surface's slope. As a consequence, previously proven results for space-like paths will hold in the whole space-time except along the slow curves.

Appeared in

  • J. Stat. Mech. Theory Exp., (2008) pp. P07022/1-P07022/18.

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