We review power laws in financial economics. This is a chapter from a preliminary draft of a book called “Beyond equilibrium and efficiency”. While some of the discussion is specific to economics, most of it applies to power laws in general – the nouns may change, but the underlying questions are similar in many fields. This draft is still preliminary and not entirely finished – comments at any...

It has long been thought that the Internet, and its constituent networks, are hierarchical in nature. Consequently, the network topology generators most widely used by the Internet research community, GT-ITM [7] and Tiers [11], create networks with a deliberately hierarchical structure. However, recent work by Faloutsos et al. [13] revealed that the Internet’s degree distribution — the distribu...

The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binaryvalued features. Recent work has provided stick-breaking representations for the beta process analogous to the ...

What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global net...

We consider the stochastic analysis of information ranking algorithms of large interconnected data sets, e.g. Google’s PageRank algorithm for ranking pages on the World Wide Web. The stochastic formulation of the problem results in an equation of the form R D = Q+ N X

P aul Samuelson (1969) was once asked by a physicist for a law in economics that was both nontrivial and true. This is a difficult challenge, as many (roughly) true results are in the end rather trivial (for example, demand curves slope down), while many nontrivial results in economics in fact require too much sophistication and rationality on the part of the agents to actually hold true in pra...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...

Casualty counts are often controversial, and thorough research can only go so far in resolving such debates—there will almost always be missing data, and thus, a need to draw inferences about how comprehensively violence has been recorded. This article addresses that challenge by developing an estimation strategy based on the observation that violent events are generally distributed according t...

Pareto, Zipf and numerous subsequent investigators of inverse power distributions have often represented their findings as though their data conformed to a power law form for all ranges of the variable of interest. I refer to this ideal case as a strong inverse power law (SIPL). However, many of the examples used by Pareto and Zipf, as well as others who have followed them, have been truncated ...

Empirical studies of real world networks revealed that degree distribution often follows a heavytailed distribution, a power law. At that time, there were two kinds of network models: the Erdos-Renyi random graph Gn,p and the Small World graphs of Watts and Strogatz. In both models the degrees were very close to the mean degree and there was little variation. Thus, there was the question of fin...