Related papers: Truncated Connectivities in a highly supercritical…
This study presents a comprehensive investigation of anisotropy in a holographic p-wave superconductor model, revealing novel insights into the behavior of quantum information measures in strongly coupled systems. Through rigorous…
The influence of anisotropy on the transport current in MgB$_2$ polycrystalline bulk samples and wires is discussed. A model for the critical current density is proposed, which is based on anisotropic London theory, grain boundary pinning…
A conjecture, known as the Shokurov-Koll\'ar connectedness principle, predicts the following. Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$; then, for any point $s \in S$, the…
We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-\alpha} for some \alpha>0.…
Based on extensive simulations, we conjecture that critically pinned interfaces in 2-dimensional isotropic random media with short range correlations are always in the universality class of ordinary percolation. Thus, in contrast to…
Azimuthal anisotropy ($v_2$) and two-particle angular correlations of high $p_T$ charged hadrons have been measured in Au+Au collisions at $\sqrt{s_{NN}}$=130 GeV for transverse momenta up to 6 GeV/c, where hard processes are expected to…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
In graph bootstrap percolation, edges of an Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$ are initially active. Activation spreads to other edges of the complete graph $K_n$ by an iterative process governed by a fixed graph $H$,…
We consider an inhomogeneous oriented percolation model introduced by de Lima, Rolla and Valesin. In this model, the underlying graph is an oriented rooted tree in which each vertex points to each of its $d$ children with `short' edges, and…
We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.
We consider a four-vertex model introduced by B\'{a}lint T\'{o}th: a dependent bond percolation model on $\mathbb{Z}^2$ in which every edge is present with probability 1/2 and each vertex has exactly two incident edges, perpendicular to…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a…
We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences…
Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to…
In high dimensional percolation at parameter $p < p_c$, the one-arm probability $\pi_p(n)$ is known to decay exponentially on scale $(p_c - p)^{-1/2}$. We show the same statement for the ratio $\pi_p(n) / \pi_{p_c}(n)$, establishing a form…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value…
We consider supercritical long-range percolation on transitive graphs of polynomial growth. In this model, any two vertices $x$ and $y$ of the underlying graph $G$ connect by a direct edge with probability $1-\exp(-\beta J(x,y))$, where…
We show that a two-band model with ${\bf k}$-dependent superconducting gaps well describes the transmission and optical conductivity measured for MgB$_2$ thin films. It is also shown that the two-band anisotropic model consistently…
In the bootstrap percolation model, sites in an $L$ by $L$ square are initially independently declared active with probability $p$. At each time step, an inactive site becomes active if at least two of its four neighbours are active. We…