The moments of the characteristic determinants of random matrices are computed here as limits, at coinciding points, of multi-point correlators of determinants. An equivalent behaviour and prefactor had been found, as a conjecture, within number theory. it is independent of the specific probability distribution. For instance, the moments of order 2 K scale, for unitary invariant ensembles, as the density of eigenvalues raised to the power K 2 the prefactor turns out to be a universal number, i.e. It turns out that these expectation values are quite interesting. ![]() It is interesting to compare the average moments of these functions in an interval to their counterpart in random matrices, which are the expectation values of the characteristic polynomials of the matrix. Number theorists have studied extensively the connections between the distribution of zeros of the Riemann ΞΆ-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |