Related papers: Crossing exponent in the Brownian loop soup
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…
Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.
We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We…
We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value…
Recently, the diffusion-limited cluster aggregation (DLCA) model was restudied as a real-world example of showing discontinuous percolation transitions (PTs). Because a larger cluster is less mobile in Brownian motion, it comes into contact…
The structural properties of additive binary hard-sphere mixtures are addressed as a follow-up of a previous paper [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)]. The so-called rational-function approximation method and an approach…
We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional…
This work continues the study started in \cite{Povolotsky2021}, where the exact densities of loops in the O(1) dense loop model on an infinite strip of the square lattice with periodic boundary conditions were obtained. These densities are…
In this paper we study the existence phase transition of scale invariant random fractal models. We determine the exact value of the critical point of this phase transition for all models satisfying some weak assumptions. In addition, we…
We examine the group formation and subsequent dynamics of active particles which are equipped with a visual perception using Langevin dynamics simulations. These particles possess an orientational response to the position of the nearest…
Multiple-quantum coherence (MQC) spectroscopy is a powerful technique for probing spin clusters, offering insights into diverse materials and quantum many-body systems. However, prior experiments have revealed a rapid decay in MQC…
This paper is concerned with the asymptotics of resonances in the semiclassical limit $h\to 0^+$ for $2\times 2$ matrix Schr\"odinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories…
We study Bernoulli first-passage percolation (FPP) on the triangular lattice $\mathbb{T}$ in which sites have 0 and 1 passage times with probability $p$ and $1-p$, respectively. Denote by $\mathcal {C}_{\infty}$ the infinite cluster with…
The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition…
The question of understanding the scaling limit of metric graph critical loop soup clusters and its relation to loop soups in the continuum appears to be one of the subtle cases that reveal interesting new scenarios about scaling limits,…
Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field…
Let $S^{d-1}_r$ be the sphere in $\bR^d$ whose center is the origin and the radius is $r$, and $\sigma_r$ be the first hitting time to it of the standard Brownian motion $\{B_t\}_{t\geqq0}$, possibly with constant drift. The aim of this…
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…
We consider the plane elasticity problem for two circular holes. When two holes are close to touching, the stress concentration happens in the narrow gap region. In this paper, we characterize the stress singularity between the two holes by…
Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…