Related papers: Harmonic Measure for Percolation and Ising Cluster…
The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the…
We suggest treating a conducting network of oriented polymer chains as an anisotropic fractal whose dimensionality D=1+\epsilon is close to one. Percolation on such a fractal is studied within the real space renormalization group of Migdal…
Every halo finding algorithm must make a critical yet relatively arbitrary choice: it must decide which structures are parent halos, and which structures are sub-halos of larger halos. We refer to this choice as ${\it percolation}$. We…
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find…
Measurements of the galaxy density and weak-lensing profiles of galaxy clusters typically rely on an assumed cluster center, which is taken to be the brightest cluster galaxy or other proxies for the true halo center. Departure of the…
The upper estimate of the percolation threshold of the Bernoulli random field on the hexagonal lattice is found. It is done on the basis of the cluster decomposition. Each term of the decomposition is estimated using the number estimate of…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…
A precise measurement of the inclusive deep-inelastic e^+p scattering cross section is reported in the kinematic range 1.5<= Q^2 <=150 GeV^2 and 3*10^(-5)<= x <=0.2. The data were recorded with the H1 detector at HERA in 1996 and 1997, and…
Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC…
The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two…
We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations…
We show how methods from Hamiltonian Floer theory can be used to establish lower bounds for the number of different time-periodic measures of time-periodic Hamiltonian systems with diffusion. After proving the existence of closed random…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We examine the potential for gamma-ray conversion to electron-positron pairs, either in the field of a nucleus or of an electron of a detector, to measure the fraction P of linear polarization of cosmic gamma sources. For this purpose we…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We present a probabilistic approach for the study of systems with exclusions, in the regime traditionally studied via cluster-expansion methods. In this paper we focus on its application for the gases of Peierls contours found in the study…
We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using…
We present the results of a QCD fit to global data on deep-inelastic polarised lepton-hadron scattering. We find that it is possible to fit the data with strongly broken SU(2) flavour for the polarised sea densities. This can easily be…
Inclusive e^\pm p single and double differential cross sections for neutral (NC) and charged current (CC) deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of…