Zobrazeno 1 - 10
of 505
pro vyhledávání: '"82B27"'
Autor:
Duminil-Copin, Hugo, Panis, Romain
This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d>6$. We obtain an upper bound for the full-space and half-space two-point functions in the critical and near-critical r
Externí odkaz:
http://arxiv.org/abs/2410.03647
Autor:
Biskup, Marek, Huang, Haiyu
Given a square box $\Lambda_n\subseteq\mathbb Z^2$ of side-length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\}$ with law proportional to ${\rm e}^{\frac12\beta(\varphi,\Delta_n\phi)}\prod_{x\in\Lambda_n}\nu(
Externí odkaz:
http://arxiv.org/abs/2412.08964
Autor:
Liu, Yucheng, Slade, Gordon
We consider spread-out models of lattice trees and lattice animals on $\mathbb Z^d$, for $d$ above the upper critical dimension $d_{\mathrm c}=8$. We define a correlation length and prove that it diverges as $(p_c-p)^{-1/4}$ at the critical point $p_
Externí odkaz:
http://arxiv.org/abs/2412.05491
Autor:
Liu, Yucheng
We consider the convolution equation $(\delta - J) * G = g$ on $\mathbb R^d$, $d>2$, where $\delta$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as $( x \cdot
Externí odkaz:
http://arxiv.org/abs/2411.16058
Autor:
Li, Zenghu, Zhang, Run
We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). We show that the class of geometric-type distributions are preserved by the model with ge
Externí odkaz:
http://arxiv.org/abs/2411.13068
Autor:
Akgün, Hakan, Yan, Xianquan, Taşkıran, Tamer, Ibrahimi, Muhamet, Mobaraki, Arash, Lee, Ching Hua, Jahangirov, Seymur
Conway's Game of Life (GOL) is an epitome showing how complex dynamical behavior emerges from simple local interactions. Although it has often been found that GOL dynamics lies close to critical behavior, this system has never been studied in the con
Externí odkaz:
http://arxiv.org/abs/2411.07189
Autor:
Camia, Federico, Feng, Yu
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight $2$, which is related to the critical Ising model. We consider the model on the plane and on domains conformally e
Externí odkaz:
http://arxiv.org/abs/2411.01467
Autor:
Gassmann, Loïc, Manolescu, Ioan
By the FKG inequality for FK-percolation, the probability of the alternating two-arm event is smaller than the product of the probabilities of having a primal arm and a dual arm, respectively. In this paper, we improve this inequality by a polynomial
Externí odkaz:
http://arxiv.org/abs/2410.23013
Autor:
Duminil-Copin, Hugo, Panis, Romain
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $d>4$. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critica
Externí odkaz:
http://arxiv.org/abs/2410.03649
Autor:
Markering, Maarten
We construct the two-sided infinite self-avoiding walk (SAW) on $\mathbb{Z}^d$ for $d\geq5$ and use it to prove pattern theorems for the self-avoiding walk. We show that infinite two-sided SAW is the infinite-shift limit of infinite one-sided SAW and
Externí odkaz:
http://arxiv.org/abs/2410.01507