THE ECONOPHYSICS OF SIZE
Holon Institute of Technology
In this talk we amalgamate ideas and concepts from various scientific disciplines – economics, mathematics, physics, probability, and statistics – to explore a topic of wide scientific interest: the omnipresence of power-laws in the distributions of sizes, commonly referred to as "Zipf’s law" and as "Pareto’s law". The talk is based on an ongoing collaboration with Morrel Cohen (Princeton & Rutgers), and is split into two parts which are outlined as follows.
Part I. Prolog: Rank distributions and Zipf’s Law:
- Lorenz’s curve, Pietra’s formula, and Gini’s index: measuring the distribution of wealth and social inequality
- Pareto’s Law: from absolute monarchy to pure communism
- Lorenzian analysis of rank distributions
- Regular variation
- Lorenzian limit law for rank distributions: the universality classes of absolute monarchy, Pareto’s law, and pure communism
- Network's macroscopic topologies: the universality classes of total connectedness ('solid state'), fractal connectedness ('liquid range'), and total disconnectedness (gas state)
- Oligarchic limit law for rank distributions: the universality classes of totalitarianism, criticality, and egalitarianism
- Interlaced universal macroscopic classification of rank distributions and their phase transitions
- Zipfian epilog: egalitarianism, totalitarianism, and criticality
Part II. Prolog: from the single-exponent Zipf Law to the double-exponent composite Zipf Law:
- Lorenzian analysis of rankdistributions
- Macroscopic structures of rank distributions:absolute monarchy and versatility
- Mapping between rankdistributions and probability laws, power-law connections
- Oligarchic analysis of rank distributions: the universality classesof totalitarianism, criticality, and egalitarianism
- Totalitarianism: absolute monarchy and monarchic clans
- Heapsian analysis of rank distributions: information streams andinnovations
- The Heaps process and the Heaps curve: a Functional Central LimitTheorem
- The Heaps curve and Laplace transforms, power-lawconnections
- Composite Zipfian epilog: Pareto and Inverse-Paretolimits; egalitarianism, monarchic-clan totalitarianism, andcriticality; composite Heapsian structure of innovations.
