### Uittreksel

We consider a special version of random sequential adsorption (RSA) with nearest-neighbor interaction on infinite tree graphs. In classical RSA, starting with a graph with initially inactive nodes, each of the nodes of the graph is inspected in a random order and is irreversibly activated if none of its nearest neighbors are active yet. We generalize this nearest-neighbor blocking effect to a degree-dependent threshold-based blocking effect. That is, each node of the graph is assumed to have its own degree-dependent threshold and if, upon inspection of a node, the number of active direct neighbors is less than that node's threshold, the node will become irreversibly active. We analyze the activation probability of nodes on an infinite tree graph, given the degree distribution of the tree and the degree-dependent thresholds. We also show how to calculate the correlation between the activity of nodes as a function of their distance. Finally, we propose an algorithm which can be used to solve the inverse problem of determining how to set the degree-dependent thresholds in infinite tree graphs in order to reach some desired activation probabilities.

Taal | Engels |
---|---|

Pagina's | 302-326 |

Aantal pagina's | 25 |

Tijdschrift | Advances in Applied Probability |

Volume | 50 |

Nummer van het tijdschrift | 1 |

DOI's | |

Status | Gepubliceerd - 1 mrt 2018 |

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*Advances in Applied Probability*,

*50*(1), 302-326. DOI: 10.1017/apr.2018.14

}

*Advances in Applied Probability*, vol. 50, nr. 1, blz. 302-326. DOI: 10.1017/apr.2018.14

**Degree-dependent threshold-based random sequential adsorption on random trees.** / Meyfroyt, Thomas M.M.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - Degree-dependent threshold-based random sequential adsorption on random trees

AU - Meyfroyt,Thomas M.M.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We consider a special version of random sequential adsorption (RSA) with nearest-neighbor interaction on infinite tree graphs. In classical RSA, starting with a graph with initially inactive nodes, each of the nodes of the graph is inspected in a random order and is irreversibly activated if none of its nearest neighbors are active yet. We generalize this nearest-neighbor blocking effect to a degree-dependent threshold-based blocking effect. That is, each node of the graph is assumed to have its own degree-dependent threshold and if, upon inspection of a node, the number of active direct neighbors is less than that node's threshold, the node will become irreversibly active. We analyze the activation probability of nodes on an infinite tree graph, given the degree distribution of the tree and the degree-dependent thresholds. We also show how to calculate the correlation between the activity of nodes as a function of their distance. Finally, we propose an algorithm which can be used to solve the inverse problem of determining how to set the degree-dependent thresholds in infinite tree graphs in order to reach some desired activation probabilities.

AB - We consider a special version of random sequential adsorption (RSA) with nearest-neighbor interaction on infinite tree graphs. In classical RSA, starting with a graph with initially inactive nodes, each of the nodes of the graph is inspected in a random order and is irreversibly activated if none of its nearest neighbors are active yet. We generalize this nearest-neighbor blocking effect to a degree-dependent threshold-based blocking effect. That is, each node of the graph is assumed to have its own degree-dependent threshold and if, upon inspection of a node, the number of active direct neighbors is less than that node's threshold, the node will become irreversibly active. We analyze the activation probability of nodes on an infinite tree graph, given the degree distribution of the tree and the degree-dependent thresholds. We also show how to calculate the correlation between the activity of nodes as a function of their distance. Finally, we propose an algorithm which can be used to solve the inverse problem of determining how to set the degree-dependent thresholds in infinite tree graphs in order to reach some desired activation probabilities.

KW - Analytical model

KW - counter-based gossip protocol

KW - interacting particle system

KW - jamming limit

KW - random sequential adsorption

KW - random tree graph

UR - http://www.scopus.com/inward/record.url?scp=85044119037&partnerID=8YFLogxK

U2 - 10.1017/apr.2018.14

DO - 10.1017/apr.2018.14

M3 - Article

VL - 50

SP - 302

EP - 326

JO - Advances in Applied Probability

T2 - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 1

ER -