Related papers: Sharp phase transition for Cox percolation
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large weights occur with higher probability. This allows the study…
We investigate the percolation properties of equatorial strips in the two-dimensional O(3) nonlinear $\sigma$ model. We find convincing evidence that such strips do not percolate at low temperatures, provided they are sufficiently narrow.…
We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we…
Conditions sufficient for the transience of the process have been established for the Markov diffusion model with switching and two modes, transient and ergodic, with intensities bounded away from zero. This paper shows limitations on the…
We provide the sharp surface density threshold to guarantee mobile sampling in terms of the surface density of the set.
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…
The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. If the phase transition of the model is second order, it can be equivalently described as a percolation transition of…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…
The circuit complexity of time-evolved pure quantum states grows linearly in time for an exponentially long time. This behavior has been proven in certain models, is conjectured to hold for generic quantum many-body systems, and is believed…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
We perform a non-perturbative study of the Coleman-Weinberg phase transition in scalar QED. Our method permits a consistent treatment of the effective potential near the origin, a region not accessible to perturbation theory. As a result,…
Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/\nu}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…
Classical bond percolation theory studies the conditions for a given point in a random graph to be connected to infinity, or "escape" to infinity, via a sequence of random edges. In this work, we present a higher-dimensional generalization…
In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch in arXiv:1010.5338 . This model features a very strong dependency structure, making it difficult to study,…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…