Apr

3

A new theory shows how wealth, in different forms, can stick to some but not to others. The findings have implications ranging from the design of the Internet to economics.

Real-world data — whether distributions of wealth, size of earthquakes or number of connections on a computer network — often follow power-law distributions rather than the familiar bell-shaped curve. In a power-law distribution, large events are reasonably common compared to smaller events.

Networks often show power laws. They can be caused by the "rich get richer" effect, also known as "preferential attachment," where nodes gain new connections in proportion to how many they already have. That means some nodes end up with many more connections than others. The phenomenon is well known, but had been assumed to be just a fundamental property of networks.

They could make tradeoffs between the network distance between nodes and the number of connections between them. By tweaking the conditions, they could make preferential attachment — a power-law distribution of the number of connections — stronger or weaker.

These tradeoffs in networks are an underlying principle behind preferential attachment, D'Souza said. The general framework could be extended to all kinds of different networks, in biology, engineering, computer science or social sciences.

From Vincent Andres:

All those people are more or less working on the same theme recently brought to our attention by Rich Bubb (March 5, 2007). This topic resonated strongly with some of my own previous work, so I did a little survey. Here are some links on those topics.

  1. Laboratoire de Physique Théorique et Modeles Statistiques
  2. Where Are the Exemplars?
  3. Review Pour La Science

Among many interesting papers, there is a nice one from M. Mezard and another nice one from JP Bouchaud.

I would be surprised if such algorithms had no application in markets. 


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