We study height and roughness distributions of films grown with discrete KardarParisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes 8 ≤ r ≤ 128 gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of ...

This paper builds upon the research of Corwin and Knizel who proved existence stationary measures for KPZ equation on an interval characterized them through a Laplace transform formula. Bryc, Kuznetsov, Wang Wesolowski found probabilistic description in terms Doob some Markov kernels; essentially at same time, another connecting to exponential functionals Brownian motion appeared work Barraquan...

Hierarchic trees with branching number close to one: noiseless KPZ equation with additional linear term for imitation of 2-d and 3-d phase transitions. Abstract An imitation of 2d field theory is formulated by means of a model on the hierarhic tree (with branching number close to one) with the same potential and the free correlators identical to 2d correlators ones. Such a model carries on some...

We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a RSOS discretization of the surface. We measure the critical exponents very precisely, and we show that the rational guess is not appropriate, and that 4D is not the upper critical dimension. We are also able to determine very precisely the exponent of the sub-leading scaling corrections, that turns out to be close to 1 ...

In this paper, we rigorously construct 2d Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov Quantum Geometry of bosonic strings. We also establish some of its fundamental properties like conformal covariance under PSL2(C)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quant...

There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar–Parisi–Zhang (KPZ) in dimension d≥3 as smoothing parameter is switched off, but most of results did not hold full temperature regions where they should. Inspired by martingale techniques coming from directed polymers literature, we first extend law large numbers for SHE obtained Mukherjee e...

We study the model of a driven interface m a disordered medium including the KPZ-nonlinearity The coupled functional renormalization group flow equations for the disorder correlator and the coupling constant associated with the KPZ-nonlinearity

The controversy whether or not the Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above which the equation does not have a strong coupling solution. A surprising aspect of these studies, however,...