Related papers: Rigidity percolation in a field
A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This yields an analytic expression for the equation of state, P = P(N/V,T), of wet…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
We consider the contact process on scale-free percolation, a spatial random graph model where the degree distribution of the vertices follows a power law with exponent $\beta$. We study the extinction time $\tau_{G_n}$ of the contact…
In this paper we explore first passage percolation (FPP) on the Erd\H{o}s-R\'enyi random graph $G_n(p_n)$, where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when $np_n\to \lambda>1,$ we…
We investigate Gabor frames on locally compact abelian groups with time-frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a…
We study the bond percolation on finite graphs induced by the level-sets of zero-average Gaussian free field on the associated metric graph above a given height (level) parameter $h \in \mathbb{R}$. We characterize the near- and…
We present a solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. It is achieved using a cavity or message passing approach, which allows one to…
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is…
I consider p-Bernoulli bond percolation on graphs of vertex-transitive tilings of the hyperbolic plane with finite sided faces (or, equivalently, on transitive, nonamenable, planar graphs with one end) and on their duals. It is known…
We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredients: (i) from the barely subcritical regime to the critical…
We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes (PPPs) in $\bbR ^2$ of intensities $\lambda$ and $\lambda_E$…
We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis…
The decay rate $\gam$ of an excited dipole molecule inside a waveguide is evaluated for the strongly coupled matter-field case near a cutoff frequency $\ome_c$ without using perturbation analysis. Due to the singularity in the density of…
In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting…
We provide a complete description of the low temperature wetting transition for the two dimensional Solid-On-Solid model. More precisely we study the integer-valued field $(\phi(x))_{x\in \mathbb Z^2}$, associated associated to the energy…
This work aims to extend the existing results on the Hausdorff dimension of the classical thick point sets of a Gaussian free field (GFF) to a more general class of exceptional sets. We adopt the circle or sphere averaging regularization to…
We consider the hard-core model in $\mathbb{R}^2$, in which a random set of non-intersecting unit disks is sampled with an intensity parameter $\lambda$. Given $\varepsilon>0$ we consider the graph in which two disks are adjacent if they…