Related papers: Conformal Invariance of Iso-height Lines in two-di…
The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter kappa equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has…
We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The…
We study atypically large fluctuations of height $H$ in the 1+1-dimensional Kardar-Parisi-Zhang (KPZ) equation at long times $t$, when starting from a "droplet" initial condition. We derive exact large deviation function of height for…
Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental…
We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…
We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition…
We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…
Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…
We study the short-time behavior of the probability distribution $\mathcal{P}(H,t)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension. The process starts from a stationary interface: $h(x,t=0)$…
We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve…
We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…
Local roughness distributions (LRDs) are studied in the growth regimes of lattice models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 and 2+1 dimensions and in a model of the Villain-Lai-Das Sarma (VLDS) growth class in 2+1 dimensions. The…
Revealing universal behaviors is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces, of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same…
Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…
We investigate the steady state phase diagram of two-component driven open condensates in one dimension. We identify a miscible-immiscible transition which is predominantly driven by gapped density fluctuations and occurs upon increasing…
The effect of geometry in the statistics of \textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield a split of them into subclasses. In this work, we…
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is ill-posed because the nonlinearity is marginally defined with respect to the roughness of the forcing noise. However, its Cole-Hopf solution,…
We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the…
We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…
We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…