Extreme Events in Stochastic Transport on Networks

Extreme events often tend to be associated with natural disasters such as the floods, droughts and earthquakes. However, more generally, any event whose magnitude displays pronounced deviation from its typical average value can be regarded as an extreme event. This definition includes events ranging from traffic congestion to powerblack-outs. In particular, many of these extreme events take place on the topology of a network. Hence, it is of interest to study how the network structure affects extreme event properties, and if these networks, as a whole unit, can survive the onslaught of extreme events taking place on them. Earlier, extreme events on the nodes of a complex network had been studied using the paradigm of random walks on complex networks. Surprisingly, it was found that extreme event occurrence probability was lower for the hubs when compared to the small degree nodes of the network. In this work, we show that the extreme event probability on the edges is a constant, and is dependent only on the parameters such as the total number of edges and the number of walkers. Furthermore, the correlation between the extreme events on the edges and nodes that they link have been studied. The non-trivial correlations indicate the role played by network structure even though the dynamics itself is that of random walkers with no memory effects.

This work was done in collaboration with Suman Kulkarni, an undergraduate student at IISER Pune and with Prof. M. S. Santhanam. The official link to the paper can be obtained from this link while freely available preprints can be found here and here.