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pro vyhledávání: '"long-range percolation"'
Autor:
Bäumler, Johannes
Consider independent long-range percolation on $\mathbb{Z}^d$ for $d\geq 3$. Assuming that the expected degree of the origin is infinite, we show that there exists an $N\in \mathbb{N}$ such that an infinite open cluster remains after deleting all edg
Externí odkaz:
http://arxiv.org/abs/2410.00303
Autor:
Khorunzhiy, O.
We study cumulants of $q$-step walks and $3$-step closed walks on Erd\"os-R\'enyi-type random graphs of long-range percolation radius model in the limit when the number of vertices $N$, concentration $c$, and the interaction radius $R$ tend to infini
Externí odkaz:
http://arxiv.org/abs/2407.11667
Autor:
Mönch, Christian
We provide a sufficient criterion for the recurrence of spatial random graphs on the real line based on the scarceness of long-edges. In particular, this complements earlier recurrence results obtained by Gracar et al. (Electron. J. Probab. 27 (2022)
Externí odkaz:
http://arxiv.org/abs/2408.06918
In this work, we study the critical long-range percolation on $\mathbb{Z}$, where an edge connects $i$ and $j$ independently with probability $1-\exp\{-\beta |i-j|^{-2}\}$ for some fixed $\beta>0$. Viewing this as a random electric network where each
Externí odkaz:
http://arxiv.org/abs/2405.03460
Autor:
Hutchcroft, Tom
In long-range percolation on $\mathbb{Z}^d$, we connect each pair of distinct points $x$ and $y$ by an edge independently at random with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta\geq 0$ is a parameter. In a
Externí odkaz:
http://arxiv.org/abs/2404.07276
Autor:
Berger, Noam, Tokushige, Yuki
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of d
Externí odkaz:
http://arxiv.org/abs/2403.18532
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Autor:
Bäumler, Johannes
We show that for long-range percolation with polynomially decaying connection probabilities in dimension $d\geq 2$, the critical value depends continuously on the precise specifications of the model. Among other things, we use this result to show tra
Externí odkaz:
http://arxiv.org/abs/2312.04099
Autor:
Bäumler, Johannes
We study independent long-range percolation on $\mathbb{Z}^d$ where the nearest-neighbor edges are always open and the probability that two vertices $x,y$ with $\|x-y\|>1$ are connected by an edge is proportional to $\frac{\beta}{\|x-y\|^s}$, where $
Externí odkaz:
http://arxiv.org/abs/2311.14352
Akademický článek
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