Related papers: Scaling limit and cube-root fluctuations in SOS su…
We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields…
Materials tuned to a quantum critical point display universal scaling properties as a function of temperature $T$ and frequency $\omega$. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of…
Data of skewness $S$ and kurtosis $K$ of vertical velocity in the convective boundary layer from different datasets have been analysed. Vertical profiles of $S$ were found to be grouped into two classes that display different slopes with…
We study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter p(N) vary with the size N of the box that one is considering, three possibilities arise in…
We consider a two-layer Heisenberg antiferromagnet which can be either in the N\'{e}el-ordered or in the disordered phase at $T=0$, depending on the ratio of the intra- and interlayer exchange constants. We reduce the problem to an…
Random systems of curves exhibiting fluctuating features on arbitrarily small scales ($\delta$) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on the probabilities of crossing events imply…
The solid-on-solid (SOS) model of an interface separating two phases is exactly soluble in two dimensions (d=2) when the interface becomes a one-dimensional string. The exact solution in terms of the transfer matrix is recalled and the…
We estimated the Galactic model parameters for a set of 36 high-latitude fields included in the currently available Data Release 5 (DR 5) of the Sloan Digital Sky Survey ({\em SDSS}), to explore their possible variation with the Galactic…
The spatial scaling law and intermittency of the $V_2 O_5$ surface roughness by atomic force microscopy has been investigated. The intermittency of the height fluctuations has been checked by two different methods, first, by measuring…
The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…
We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size…
We address the system-size dependence of typical plastic flow events when an amorphous solid is put under a fixed external strain rate at a finite temperature. For system sizes that are accessible to numerical simulations at reasonable…
Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that…
We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…
For a family of bond percolation models on Z^{2} that includes the Fortuin-Kasteleyn random cluster model, we consider properties of the ``droplet'' that results, in the percolating regime, from conditioning on the existence of an open dual…
We prove that large Boltzmann stable planar maps of index $\alpha \in (1;2)$ converge in the scaling limit towards a random compact metric space $\mathcal{S}_{\alpha}$ that we construct explicitly. They form a one-parameter family of random…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
The low-temperature series for the surface width of the Absolute value Solid-On-Solid model and the Discrete Gaussian model both on the square lattice and on the triangular lattice are generated to high orders using the improved…
We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…
We consider scaling limits of random quadrangulations obtained by applying the Cori-Vauquelin-Schaeffer bijection to Bienaym\'e-Galton-Watson trees with stably-decaying offspring tails with an exponent $\alpha$ in (1, 2). We show that these…