Pioneers on a New Continent:
Crossing the Ocean between Physics and Economics

Sorin Solomon
Hebrew University of Jerusalem

The manifest destiny and the ultimate frontier for the physicists on the financial markets continent is to investigate the birth of complex macroscopic market dynamics out of the microscopic individual traders' interactions. Their main tool is statistical mechanics, which has been routinely used lately by physicists for expansion in various complex fields beyond traditional physics frontiers.

In such excursions outside the Physics lands one often encounters "exotic" stochastic systems consisting of many autocatalytic parts. For instance, the wealth of the individual traders, the market capitalization of each firm in the market, and the number of investors adopting a common investment strategy, are all stochastically autocatalytic in the sense that their jumps (elementary quanta of change), from one time instant to the next, are typically proportional (via stochastic factors) to their current value.

Even though such systems are rare in physics, advanced statistical mechanics techniques do apply to them and turned out to have crucial relevance: while the usual partial differential equations treatment of these systems often predicts a "dead" trade-less market, the renormalization group "corrections" insure the emergence of a macroscopic adaptive collective dynamics which allows the survival and development of a lively robust market.

Stochastic autocatalytic growth generates even in very non-stationary logistic systems robust Pareto-Zipf power-law wealth distributions. It was shown that it if the market is efficient, one can map it onto a statistical mechanics system in thermal equilibrium. Consequently, the Pareto law emerges in efficient markets as universally as the Boltzmann law holds universally for all systems in thermal equilibrium.

I will illustrate the issues of principle with practical market examples chosen from the work of various "econophysics" groups.