Related papers: Equal-time correlation function for directed perco…
We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary…
By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few…
We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we…
Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…
Correlation function is defined and calculated for the punctual states of the fermion supersymmetric string (N=1), in its critical dimension D=10.
The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation…
We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…
We propose a self-contained and accessible derivation of an exact formula for the $n$-point correlation functions of the signal measured when continuously observing a quantum system. The expression depends on the initial quantum state and…
We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation…
We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a…
Fitting percolation into the conformal field theory framework requires showing that connection probabilities have a conformally invariant scaling limit. For critical site percolation on the triangular lattice, we prove that the probability…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We present some exact results on the behavior of Branching and Annihilating Random Walks, both in the Directed Percolation and Parity Conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the…
Correlation factors are constructed that are consistent with the permutation symmetry group of N Fermions at given value of the filling factor.
We show that oriented percolation occurs whenever a condition is satisfied called "exponential intersection tails". This condition says that a measure on paths exists for which the probability of two independent paths intersecting in more…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We discuss the various definitions of time correlation functions and how to estimate them from experimental or simulation data. We start with the various definitions, both in real and in Fourier space, and explain how to extract from them a…
Random percolation can be fully interpreted as a confining pure gauge theory. With numerical high-precision measurements of Polyakov-Polyakov correlators at finite temperature, we could well observe the presence of shape effects due to…
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…