# Regensburg 2013 – wissenschaftliches Programm

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# SOE: Fachverband Physik sozio-ökonomischer Systeme

## SOE 12: Risks and Large Deviations in Economic Networks II

### SOE 12.1: Vortrag

### Dienstag, 12. März 2013, 11:45–12:00, H37

**Large-deviation properties of simple energy-grid models** — •Alexander K. Hartmann — Institute of Physics, University of Oldenburg

Here the large-deviation properties of a simple
model of the stability of energy grids and other transport
networks are studied numerically [1]. The model is based an the shortest-path edge centrality
which is used to estimate the amount of additional reserve capacity
which must be available to prevent cascading failures upon the
failure of the most important connections. The large-deviation
properties of the distribution of this reserve capacity are obtained using
specifically biased [2] Monte Carlo simulations. This allows to
obtain the distribution easily in regions where the
probabilities are as small as
10^{−40}. In particular the most resilient (optimum) as
well as the least resilient (worst) networks are obtained
during the simulations.
The results, in particular fits to assess the
shape of the distributions are obtained for different graph ensembles
like two-dimensional diluted grids, Small-World networks and
Erdős-Rényi random graphs.

[1] A.K. Hartmann, *Practical Guide to Computer Simulations* (World-Scientific, Singapore, 2009)

[2] A.K. Hartmann, Sampling rare events: statistics of local sequence alignments, Phys. Rev. E **65**, 056102 (2002)