An Urn Model for Cascading Failures on a Lattice

Cirillo, Pasquale; Hüsler, Jürg (2012). An Urn Model for Cascading Failures on a Lattice. Probability in the engineering and informational sciences, 26(4), pp. 509-534. New York, N.Y.: Cambridge University Press 10.1017/S0269964812000162

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A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

Item Type:

Journal Article (Original Article)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Cirillo, Pasquale and Hüsler, Jürg




Cambridge University Press




Lutz Dümbgen

Date Deposited:

04 Oct 2013 14:42

Last Modified:

26 Oct 2019 09:06

Publisher DOI:


Web of Science ID:




URI: (FactScience: 224963)

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