Related papers: Limit theorems for 2D invasion percolation
We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…
Crossing probabilities for critical 2-D percolation on large but finite lattices have been derived via boundary conformal field theory. These predictions agree very well with numerical results. However, their derivation is heuristic and…
We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in…
The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular $d$-dimensional hypercubic lattices are in the present work investigated using the…
In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…
We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…
We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches…
In the hard pomeron theory with the number of colours Nc in the infinity limit the diffractive amplitude obtained in [3] is compared with the results found for Nc=3 in [1] and in the dipole approach in [5]. It is shown that the double…
We present a concentration result concerning random weighted projections in high dimensional spaces. As applications, we prove (1) New concentration inequalities for random quadratic forms; (2) The infinity norm of most unit eigenvectors of…
We use invasion percolation to compute highly-accurate numerical values for bond and site percolation thresholds p_c on the hypercubic lattice Z^d for d = 4,,,,,13. We also compute the Fisher exponent tau governing the cluster size…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
We study a percolation problem based on critical loop configurations of the O($n$) loop model on the honeycomb lattice. We define dual clusters as groups of sites on the dual triangular lattice that are not separated by a loop, and…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…
We introduce a notion of capacity for high dimensional critical percolation by showing that for any finite set $A$, the suitably rescaled probability that the cluster of $z$ intersects $A$ converges as $\|z\|\to\infty$. This can be viewed…
We consider first-passage percolation on the two-dimensional triangular lattice $\mathcal{T}$. Each site $v\in\mathcal{T}$ is assigned independently a passage time of either $0$ or $1$ with probability $1/2$. Denote by $B^+(0,n)$ the upper…
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…
This article deals with limit theorems for certain loop variables for loop soups whose intensity approaches infinity. We first consider random walk loop soups on finite graphs and obtain a central limit theorem when the loop variable is the…
We show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{\'e} approximants of the mean cluster number $S(p)$ for site and bond percolation on general $d$-dimensional lattices are upper bounds on this quantity in any Euclidean…