Interestingly, the behavior in the strongly disordered limit of these systems is qualitatively different. Narayan, together with Fisher, has developed a new model to treat this strongly disordered regime, establishing connections with percolation theory and predicting the existence of large scale spatial structures. Narayan has also worked on the inhomogenous distribution of forces in packed granular materials like sand, and the connection to models of river basins. Although the two problems are superficially very different, the latter emerges as a critical point of the former. The methods used by Narayan are primarily analytical, supplemented by numerical simulations when needed.
Emphasis is placed both on the construction and analysis of appropriate simple physical models.
In addition, Narayan has worked on several other problems in other areas. He has analyzed the effects of the long-range dependence observed in Ethernet traffic, and demonstrated that it will have significant impact on processing delays. Work is continuing in this area on interconnected networks, where more interesting phenomena like instabilities or gridlock can occur. Concepts from statistical mechanics can be applied fruitfully to these questions. He has also worked on applying random matrix theory to complicated quantum systems, and suggested an explanation for the predicted universality of the correlation functions describing the response of their energy levels to external perturbations.