I Directed polymers A Why bother? II Hamiltonian and Randomness A Pure case B Let’s put randomness 1 Hamiltonian 2 Partition function 3 Averages C What to look for? D Size: disorder and thermal correlation 1 Free energy fluctuation 2 Our Aim 3 Digression: Self-averaging III Q.: Is disorder relevant? A Annealed average: low temperature problem B Moments of Z 1 Hamiltonian for moments 2 Bound sta...

[1] Landscapes share important similarities with turbulence: both systems exhibit scale invariance (self-similarity) over a wide range of scales, and their behavior can be described using comparable dynamic equations. In particular, modified versions of the KardarParisi-Zhang (KPZ) equation (a low-dimensional analog to the Navier-Stokes equations) have been shown to capture important features o...

We model the ascent of warm, moist air in the Earth’s atmosphere by turbulent convection and expansion with the KPZ equation, familiar in the physics literature on surface growth. Clouds form in domains where the interface between the rising air and its surrounding air achieves an elevation higher than that necessary for condensation. The model predictions are consistent with the perimeter frac...

We consider the dielectric breakdown model in the limit η → 0+. A differential equation describing the surface growth is derived; this equation is KPZ plus a term causing linear instability, and includes a short-distance regularization similar to a viscosity. The equation exhibits an interesting dynamics in terms of poles, permitting us to derive a large family of solutions to the equation of m...

Abstract A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with $$(1+1)$$ ( 1 + ) dimensional Kardar–Parisi–Zhang equation. In present paper, analytical results obtained...

One of the main difficulties in proving convergence discrete models surface growth to Kardar-Parisi-Zhang (KPZ) equation dimensions higher than one is that correct way take a scaling limit, so limit nontrivial, not known rigorous sense. To understand KPZ without being hindered by this issue, article introduces notion "local behavior", which roughly means instantaneous at point decomposes into s...