THE ECONOPHYSICS OF SIZE
Holon Institute of TechnologyIn 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 § Networks’ 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 rank distributions § Macroscopic structures of rank distributions: absolute monarchy and versatility § Mapping between rank distributions and probability laws, power‐law connections § Oligarchic analysis of rank distributions: the universality classes of totalitarianism, criticality, and egalitarianism § Totalitarianism: absolute monarchy and monarchic clans § Heapsian analysis of rank distributions: information streams and innovations § The Heaps process and the Heaps curve: a Functional Central Limit Theorem § The Heaps curve and Laplace transforms, power‐law connections § Composite Zipfian epilog: Pareto and Inverse‐Pareto limits; egalitarianism, monarchic‐clan totalitarianism, and criticality; composite Heapsian structure of innovations.