2007/11/30 by Satya N. Majumdar, Oriol Bohigas, Arul Lakshminarayan · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s10955-008-9491-5
published as J. Stat. Phys. 131, 33 (2008) · 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phys
arxiv created 2008/01/14 · arxiv updated 2009/12/01
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N \em strongly correlated random variables for all values of N (and not just for large N).