Critical properties of a growing interface described by the
Kardar-Parisi-Zhang equation.
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The Kardar-Parisi-Zhang equation is a stochastic non-equilibrium and non-linear
equation initially derived to describe the kinetic roughening of a growing
interface. As it has turned out to map to many other important problems, such as
directed polymers in random media or Burgers turbulence, it has  emerged as a
fundamental model to investigate non-equilibrium scaling phenomena and phase
transitions.
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The theoretical understanding of the interface properties in the rough phase,
corresponding to a strong-coupling regime, requires non-perturbative methods.
I will show,  from a detailed analysis of the KPZ symmetries, how to construct
an  effective action to study the KPZ growth,  and derive its Non-Perturbative
Renormalization Group flow. I will then present results for critical properties
in the stationary regime: critical exponents and correlation and response
functions. I will show that these functions exhibit generic scaling, determine
the associated universal scaling functions and universal amplitude ratios.