We survey a theory of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volumes. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively...

This manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena—scale invariance and universality—can be useful in guiding research on interpreting empirical data on economic fluctuations....

One challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time. We present an...

Co-movements of stock price fluctuations are described by the cross-correlation matrix C. The application of random matrix theory (RMT) allows to distinguish between spurious correlations in C due to measurement noise and true correlations containing economically meaningful information. By...

Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find...

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there...

Scale-free distributions and correlation functions found in financial data are reminiscent of the scale invariance of physical observables in the vicinity of a critical point. Here, we present empirical evidence for a transition phenomenon, accompanied by a symmetry breaking, in the investors'...

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686...