Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Heydenreich, Markus"'
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs proportionally
Externí odkaz:
http://arxiv.org/abs/2407.12484
Autor:
Dickson, Matthew, Heydenreich, Markus
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk model, the hyp
Externí odkaz:
http://arxiv.org/abs/2309.08830
Autor:
Dickson, Matthew, Heydenreich, Markus
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the two endpoint
Externí odkaz:
http://arxiv.org/abs/2210.07727
We study the high-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the direction
Externí odkaz:
http://arxiv.org/abs/2210.03174
Autor:
Hao, Nannan, Heydenreich, Markus
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices $x,y\in\mathbb{Z}^d$ are linked by an edge with probability depending on i.i.d.\ vertex weights and the Euclidean distance $|x-y|$. Depend
Externí odkaz:
http://arxiv.org/abs/2105.05709
We study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb gas in the high-temperature regime. For this, we exploit the duality
Externí odkaz:
http://arxiv.org/abs/2103.11985
We study the sizes of the Voronoi cells of $k$ uniformly chosen vertices in a random split tree of size $n$. We prove that, for $n$ large, the largest of these $k$ Voronoi cells contains most of the vertices, while the sizes of the remaining ones are
Externí odkaz:
http://arxiv.org/abs/2103.09784
Autor:
Heydenreich, Markus, Hirsch, Christian
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with max-stable distri
Externí odkaz:
http://arxiv.org/abs/2006.00747
Autor:
Heydenreich, Markus, Matzke, Kilian
We expand the critical point for site percolation on the $d$-dimensional hypercubic lattice in terms of inverse powers of $2d$, and we obtain the first three terms rigorously. This is achieved using the lace expansion.
Comment: 22 pages
Comment: 22 pages
Externí odkaz:
http://arxiv.org/abs/1912.04584
Autor:
Heydenreich, Markus, Matzke, Kilian
We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in hi
Externí odkaz:
http://arxiv.org/abs/1911.04159