This paper explores the cross-correlations between price fluctuations of different stocks using random matrix theory (RMT). The authors analyze two large databases: one with 30-minute returns of 1000 US stocks over a 2-year period (1994-1995) and another with 30-minute returns of 881 US stocks over the same period. Additionally, they examine daily returns of 422 US stocks over a 35-year period (1962-1996). They calculate the cross-correlation matrices and test the statistics of their eigenvalues against a "null hypothesis" of a random correlation matrix. The results show that most eigenvalues fall within the RMT bounds, indicating a high degree of randomness in the measured cross-correlation coefficients. However, deviations from RMT are found for a small fraction of the largest and smallest eigenvalues, suggesting genuine correlations. These deviating eigenvectors are stable over time and reveal systematic deviations from RMT predictions. The largest eigenvalue corresponds to a common influence on all stocks, while the remaining deviating eigenvectors are associated with distinct business sectors. The paper discusses the implications of these findings for portfolio optimization and risk management.This paper explores the cross-correlations between price fluctuations of different stocks using random matrix theory (RMT). The authors analyze two large databases: one with 30-minute returns of 1000 US stocks over a 2-year period (1994-1995) and another with 30-minute returns of 881 US stocks over the same period. Additionally, they examine daily returns of 422 US stocks over a 35-year period (1962-1996). They calculate the cross-correlation matrices and test the statistics of their eigenvalues against a "null hypothesis" of a random correlation matrix. The results show that most eigenvalues fall within the RMT bounds, indicating a high degree of randomness in the measured cross-correlation coefficients. However, deviations from RMT are found for a small fraction of the largest and smallest eigenvalues, suggesting genuine correlations. These deviating eigenvectors are stable over time and reveal systematic deviations from RMT predictions. The largest eigenvalue corresponds to a common influence on all stocks, while the remaining deviating eigenvectors are associated with distinct business sectors. The paper discusses the implications of these findings for portfolio optimization and risk management.