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pro vyhledávání: '"First-passage percolation"'
Autor:
Jacquet, Antonin
In the models of first-passage percolation and directed first-passage percolation on $\mathbb{Z}^d$, we consider a family of i.i.d. random variables indexed by the set of edges of the graph, called passage times. For every vertex $x \in \mathbb{Z}^d$
Externí odkaz:
http://arxiv.org/abs/2412.20779
In 1999, Zhang proved that, for first passage percolation on the square lattice $\mathbb{Z}^2$ with i.i.d. non-negative edge weights, if the probability that the passage time distribution of an edge $P(t_e = 0) =1/2 $, the critical value for bond per
Externí odkaz:
http://arxiv.org/abs/2412.03415
Autor:
Kammerer, Emmanuel
We establish the scaling limit of the geodesics to the root for the first passage percolation distance on random planar maps. We first describe the scaling limit of the number of faces along the geodesics. This result enables to compare the metric ba
Externí odkaz:
http://arxiv.org/abs/2412.02666
Autor:
Verges, Julien
Consider standard first-passage percolation on $\mathbb Z^d$. We study the lower-tail large deviations of the rescaled random metric $\widehat{\mathbf T}_n$ restricted to a box. If all exponential moments are finite, we prove that $\widehat{\mathbf T
Externí odkaz:
http://arxiv.org/abs/2412.03320
In gossip networks, a source node forwards time-stamped updates to a network of observers according to a Poisson process. The observers then update each other on this information according to Poisson processes as well. The Age of Information (AoI) of
Externí odkaz:
http://arxiv.org/abs/2409.12710
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal law of any
Externí odkaz:
http://arxiv.org/abs/2409.08882
Autor:
Bakhtin, Yuri, Dow, Douglas
We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which that limi
Externí odkaz:
http://arxiv.org/abs/2406.09652
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We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the probabili
Externí odkaz:
http://arxiv.org/abs/2407.17855