Related papers: Universal properties of the confining string in th…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from…
We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…
Simple scaling properties of correlation functions of a confining gauge theory in d-dimensions lead to the conclusion that k-string dynamics is described, in the infrared limit, by a two-dimensional conformal field theory with conformal…
We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
Using light cone string field theory we derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory. These results extend to strings in a plane wave…
The extraction of Wilson loops of confining gauge systems from their SUGRA (string) duals is reviewed. I start with describing the basic classical setup. A theorem that determines the classical values of the loops associated with a…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
The one-plaquette Hamiltonian of large N lattice gauge theory offers a constructive model of a $1+1$-dimensional string theory with a stable ground state. The free energy is found to be equivalent to the partition function of a string where…
We have calculated the running coupling in SU(2), SU(3), and SU(4) gauge theories to see whether they have infrared fixed points. An infrared fixed point means no confinement: It means that the long-distance physics is conformal, without a…
Recent progress achieved in the solution of the problem of confinement in various (non-)Abelian gauge theories by virtue of a derivation of their string representation is reviewed. The theories under study include QCD within the so-called…
In the Constrained-degree percolation model on a graph $(\mathbb{V},\mathbb{E})$ there are a sequence, $(U_e)_{e\in\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open…
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…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. Since the system is strongly…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…