Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Markus Heydenreich"'
Publikováno v:
Alea-Latin american journal of probability and mathematical statistics, 15, 233-245. IMPA
For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the first time
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c5238c4fefa3416686a4c4ee6bca50a6
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103796
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103796
Publikováno v:
Oberwolfach Reports. 16:1071-1111
Crystallisation, by which we mean the formation of solids precipitating from a solution, is the central theme of the present mini-workshop. Participants discussed different approaches towards a rigorous mathematical understanding of crystallisation a
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6c758f680b51122b86ece6fb7ef98e3
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103816
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103816
Autor:
Nannan Hao, Markus Heydenreich
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09c71c14acb5010fe88228a2ffe713dc
Autor:
Markus Heydenreich
Publikováno v:
Fractal Geometry and Stochastics VI ISBN: 9783030596484
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of \(\mathbb {R}^d\). In this expository text, we discuss their analogues for infinite subsets of \({\mathbb {Z}^d}\) and, more generally, for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3e0f77c80ddef6ceacb6987d16d53f15
https://doi.org/10.1007/978-3-030-59649-1_5
https://doi.org/10.1007/978-3-030-59649-1_5
Publikováno v:
Bernoulli 26, no. 2 (2020), 1269-1293
We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a realignment of opi
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783030484774
WAW
WAW
Weight-dependent random connection graphs are a class of local network models that combine scale-free degree distribution, small-world properties and clustering. In this paper we discuss recurrence or transience of these graphs, features that are rel
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::790d7ee65213f972f5858cea0fad8222
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103791
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/103791
Autor:
Markus Heydenreich, Christian Hirsch
Publikováno v:
Extremes, 25
Heydenreich, M & Hirsch, C 2022, ' Extremal linkage networks ', Extremes, vol. 25, no. 2, pp. 229-255 . https://doi.org/10.1007/s10687-021-00433-3
Heydenreich, M & Hirsch, C 2022, ' Extremal linkage networks ', Extremes, vol. 25, no. 2, pp. 229-255 . https://doi.org/10.1007/s10687-021-00433-3
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d9297129313fe313791e04cb5618816f
Autor:
Markus Heydenreich, Kilian Matzke
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.
22 pages
22 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::171e9c541efdc147329684e8aca0ec6d
http://arxiv.org/abs/1912.04584
http://arxiv.org/abs/1912.04584
Publikováno v:
Probability Theory and Related Fields. 175:1183-1185
In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.