Related papers: Spatial correlations of the 1D KPZ surface on a fl…
We consider pairs of maps from a discrete group to the unitary group. The deficiencies of these maps from being homomorphisms may be great, but if they are close to each other then we call such pairs balanced. We show that balanced pairs…
By using the Kirkwood formula, the friction coefficient of a solvated Brownian particle is determined from the integration on time of the autocorrelation function of the force that the solvent exerts on this particle. Extensive molecular…
For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to the largest one is governed by the Airy point process. In such ensembles, the limit distribution of the k-th largest eigenvalue is given in…
We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple…
Optimal embedding in the three-dimensional space of exponentially growing squeezed surfaces, like plants leaves, or 2D colonies of exponentially reproducing cells, is considered in the framework of conformal approach. It is shown that the…
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as…
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…
In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian…
We consider stochastic particle dynamics on hypersurfaces represented in Monge gauge parametrization. Starting from the underlying Langevin system, we derive the surface Dean-Kawasaki (DK) equation and formulate it in the martingale sense.…
We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…
We present a newly developed approach for the calculation of interfacial stiffness and contact area evolution between two rough bodies exhibiting self affine surface structures. Using spline assisted discretization to define localised…
We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and…
Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient $(D)$ of a Brownian particle on the distribution width $(\varepsilon)$ of…
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…
A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically…
Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a…
We investigate experimentally and theoretically thin layers of colloid particles held adjacent to a solid substrate by gravity. Epifluorescence, confocal, and holographic microscopy, combined with Monte Carlo and hydrodynamic simulations,…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…
We demonstrate that for the sine-Gordon theory at the free fermion point, the 2-point correlation functions of the fields $\exp (i\al \Phi )$ for $0< \al < 1$ can be parameterized in terms of a solution to a sinh-Gordon-like equation. This…