Related papers: The scaling limit of the Minimal Spanning Tree - a…

We show that the Gromov-Hausdorff-Prohorov scaling limit of a critical percolation cluster on a random hyperbolic triangulation of the half-plane is the Brownian continuum random tree. As a corollary, we obtain that a simple random walk on…

Spiral (gyrotropic) percolation which is related to the behavior of an electron system in strong magnetic fields is studied. It is shown that the scaling behavior area near the percolation threshold is anomalously narrow. The percolation…

We prove that in the scaling limit, the crossing probabilities of multiple interfaces in the critical planar Ising model with alternating boundary conditions are conformally invariant expressions given by the pure partition functions of…

Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…

We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in…

We study the alternating $k$-arm incipient infinite cluster (IIC) of site percolation on the triangular lattice $\mathbb{T}$. Using Camia and Newman's result that the scaling limit of critical site percolation on $\mathbb{T}$ is CLE$_6$, we…

We analyze the geometry of domain Markov half planar triangulations. In \cite{AR13} it is shown that there exists a one-parameter family of measures supported on half planar triangulations satisfying translation invariance and domain Markov…

Expressions for scaling limits of random walks, such as those obtained in several areas of the Probability theory literature, are of great significance in characterizing long term, stationary behavior of random processes. Presumably, in the…

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the…

We study spanners in planar domains, including polygonal domains, polyhedral terrain, and planar metrics. Previous work showed that for any constant $\epsilon\in (0,1)$, one could construct a $(2+\epsilon)$-spanner with $O(n\log(n))$ edges…

The main purpose of this paper is to study two scaling methods developed respectively by Pinchuk and Frankel. We introduce first a continuously-varying global coordinate system, and give an alternative proof to the convergence of Pinchuk's…

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard…

We briefly review the concept of scaling and how it occurs in quasielastic electron and neutrino scattering from nuclei, and then the particular approach to scaling in the short-time approximation. We show that, while two-nucleon currents…

We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…

Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which…

The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…

In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian…

The recent study by Waclawczyk et al. [Phys. Rev. Fluids 6, 084610 (2021)] on conformal invariance in 2D turbulence is misleading as it makes three incorrect claims that form the core of their work. We will correct these claims and put them…

We provide explicit conditions, in terms of the transition kernel of its driving particle, for a Markov branching process to admit a scaling limit toward a self-similar growth-fragmentation with negative index. We also derive a scaling…