Slightly subcritical hypercube percolation

Autor: Tim Hulshof, Asaf Nachmias

Publikováno v: Random Structures and Algorithms, 56(2), 557-593. Wiley

We study bond percolation on the hypercube $\{0,1\}^m$ in the slightly subcritical regime where $p = p_c (1-\varepsilon_m)$ and $\varepsilon_m = o(1)$ but $\varepsilon_m \gg 2^{-m/3}$ and study the clusters of largest volume and diameter. We establis

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0becd42b550ea66ab2ba2be9d64cc308
https://doi.org/10.1002/rsa.20853

Expansion of percolation critical points for Hamming graphs

Autor: Remco van der Hofstad, Lorenzo Federico, Tim Hulshof, Frank den Hollander

Publikováno v: Combinatorics, Probability and Computing, 29(1), 68-100. Cambridge University Press

The Hamming graph $H(d,n)$ is the Cartesian product of $d$ complete graphs on $n$ vertices. Let $m=d(n-1)$ be the degree and $V = n^d$ be the number of vertices of $H(d,n)$. Let $p_c^{(d)}$ be the critical point for bond percolation on $H(d,n)$. We s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eaf65ea79650a75cf6f2cb5d35c2096e
http://wrap.warwick.ac.uk/123712/1/WRAP-expansion-percolation-critical-points-hamming-graphs-Federico-2019.pdf

Not all interventions are equal for the height of the second peak

Autor: Joost Jorritsma, Júlia Komjáthy, Tim Hulshof

Publikováno v: Chaos, Solitons and Fractals, 139:109965. Elsevier
Chaos, Solitons, and Fractals

In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e169b824b98c6001600aabe2fc1bcd2
https://doi.org/10.1016/j.chaos.2020.109965

Structures in supercritical scale-free percolation

Autor: Tim Hulshof, Markus Heydenreich, Joost Jorritsma

Publikováno v: Ann. Appl. Probab. 27, no. 4 (2017), 2569-2604
The Annals of Applied Probability, 27(4), 2569-2604. Institute of Mathematical Statistics

Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs. recurrence

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eece494dfd12b68450ae5a1cefd61702
https://projecteuclid.org/euclid.aoap/1504080041

Finite-size effects for anisotropic bootstrap percolation

Autor: Tim Hulshof, Aernout C.D. van Enter

Publikováno v: Journal of Statistical Physics, 128(6), 1383-1389. Springer
Journal of Statistical Physics, 128(6), 1383-1389. SPRINGER

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eb08beba6f8dbfe47aaecb553be7360c
https://doi.org/10.1007/s10955-007-9377-y