A lower bound for point-to-point connection probabilities in critical percolation

Autor: J. van den Berg, Henk Don

Publikováno v: Electronic Communications in Probability, 25, 1-9
Electronic Communications in Probability, 25:47, 1-9. Institute of Mathematical Statistics
Electronic Communications in Probability, 25, pp. 1-9
Electron. Commun. Probab.
Van Den Berg, J & Don, H 2020, ' A lower bound for point-to-point connection probabilities in critical percolation ', Electronic Communications in Probability, vol. 25, 47, pp. 1-9 . https://doi.org/10.1214/20-ECP326

Consider critical site percolation on $\mathbb{Z}^d$ with $d \geq 2$. We prove a lower bound of order $n^{- d^2}$ for point-to-point connection probabilities, where $n$ is the distance between the points. Most of the work in our proof concerns a `con

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d125557a294245c623fe1f9926e1b9f
https://doi.org/10.1214/20-ecp326

Explicit bounds for critical infection rates and expected extinction times of the contact process on finite random graphs

Autor: Henk Don, Eric Cator

Publikováno v: Bernoulli, 27, 1556-1582
Bernoulli, 27, 3, pp. 1556-1582

We introduce a method to prove metastability of the contact process on Erd\H{o}s-R\'enyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed number of nodes

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10bfe2428e378f10ac7e5397f72209fc
http://hdl.handle.net/2066/233838

Slowly synchronizing automata with fixed alphabet size

Autor: Michiel de Bondt, Hans Zantema, Henk Don

Publikováno v: Information and Computation, 279, pp. 1-19
Don, H, Zantema, H & de Bondt, M 2021, ' Slowly synchronizing automata with fixed alphabet size ', Information and Computation, vol. 279, 104614, pp. 1-19 . https://doi.org/10.1016/j.ic.2020.104614
Information and Computation, 279:104614, 1-19. Elsevier Inc.
Information and Computation, 279, 1-19

It was conjectured by \v{C}ern\'y in 1964 that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. In this paper, we investigate the r

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::79b7f2fefd3a28aa39d2b261c6b747e7
http://arxiv.org/abs/1609.06853

Polygons in billiard orbits

Autor: Henk Don

Publikováno v: Journal of Number Theory. 132:1151-1163

We study the geometry of billiard orbits on rectangular billiards. A truncated billiard orbit induces a partition of the rectangle into polygons. We prove that thirteen is a sharp upper bound for the number of different areas of these polygons.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::93b373aeff376c5229b1c8d2424de8f8
https://doi.org/10.1016/j.jnt.2011.12.012

On the distribution of the distances of multiples of an irrational number to the nearest integer

Autor: Henk Don

Publikováno v: Acta Arithmetica. 139:253-264

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::00ecc94b1662da74d59f085563578349
https://doi.org/10.4064/aa139-3-4