Record statistics in random vectors and quantum chaos

Abstract

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records that is non-universal but tends to the Gumbel distribution asymptotically. The quantum standard map is used to study these statistics for the effect of correlations apart from normalization. It is seen that in the mixed phase space regime the number of intensity records is a power law in the dimensionality of the state as opposed to the logarithmic growth for random states.

figures redrawn, discussion added

References in corpus (6)

• Universal Record Statistics of Random Walks and Lévy Flights
• Record statistics for biased random walks, with an application to financial data
• Condensation and Extreme Value Statistics
• Spectral fluctuations and 1/f noise in the order-chaos transition regime
• Record Statistics of Continuous Time Random Walk
• Entanglement between two subsystems, the Wigner semicircle and extreme value statistics

Cited by in corpus (6)

• Record statistics of a strongly correlated time series: random walks and Lévy flights
• Record-breaking statistics for random walks in the presence of measurement error and noise
• Record statistics of financial time series and geometric random walks
• Records in the classical and quantum standard map
• Extreme Event Statistics in a Drifting Markov Chain
• Records and occupation time statistics for area-preserving maps