It is shown that the evolution of the density perturbations during certain eras of substantial entropy generation in the universe can be described in the scheme of the KPZ equation. Therefore, the in uence on cosmological structure formation by stochastic forces arising from various dissipations can be studied through the universal characteristics of surface growth in d = 3 + 1 dimensions. We i...

It is shown that the evolution of the density perturbations during certain eras of substantial entropy generation in the universe can be described in the scheme of the KPZ equation. Therefore, the influence on cosmological structure formation by stochastic forces arising from various dissipations can be studied through the universal characteristics of surface growth in d = 3 + 1 dimensions. We ...

We study elastic manifolds in a N -dimensional random potential using functional RG. We extend to N > 1 our previous construction of a field theory renormalizable to two loops. For isotropic disorder with O(N) symmetry we obtain the fixed point and roughness exponent to next order in = 4− d, where d is the internal dimension of the manifold. Extrapolation to the directed polymer limit d = 1 all...

In this paper, we establish the Knizhnik–Polyakov–Zamolodchikov (KPZ) formula of Liouville quantum gravity, using the heat kernel of Liouville Brownian motion. This derivation of the KPZ formula was first suggested by F. David and M. Bauer in order to get a geometrically more intrinsic way of measuring the dimension of sets in Liouville quantum gravity. We also provide a careful study of the (n...

We discuss an asymmetric energy model (AEM) introduced by Giardina et al. in [10]. This model is expected to belong to the KPZ class. We obtain lower bounds for the diffusion coefficient. In particular, the diffusion coefficient is diverging in dimension one and two as it is expected in the KPZ picture.

The statistics of the fluctuations quantum many-body systems are highly revealing their nature. In driven-dissipative displaying macroscopic coherence, as exciton polariton condensates under incoherent pumping, phase dynamics can be mapped to stochastic Kardar-Parisi-Zhang (KPZ) equation. However, it was argued theoretically that in two dimensions KPZ regime may hindered by presence vortices, a...

In this paper, connection between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a stochastic elastic forcing term −κy+η(s), on a particle moving along a rough surface. Two models are proposed and analysed in this way: the random-walk proces...