منابع مشابه
Universal shocks in random matrix theory.
We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a...
متن کاملUniversal relation between Green’s functions in random matrix theory
We prove that in random matrix theory there exists a universal relation between the one-point Green’s function G and the connected twopoint Green’s function Gc given by NGc(z,w) = ∂ ∂z∂w log(( G(z)−G(w) z−w ) + irrelevant factorized terms. This relation is universal in the sense that it does not depend on the probability distribution of the random matrices for a broad class of distributions, ev...
متن کاملUniversality in Random Matrix Theory
which is the Central Limit Theorem. In principle, all the random variables X1, X2, · · · , XN can be of order 1, hence SN ∼ 1 as well, but the probability of having such a rare event is incredibly small. We can even estimate the bound on the probability for the rare event from the large deviation principle. A similar phenomenon happens when we form a large matrix from i.i.d. random variables an...
متن کاملDevelopments in Random Matrix Theory
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.
متن کاملRandom Matrix Theory
Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1] • A. Guionnet. Large random matrices: lectures on macroscopic asymptotics. • M. L. Mehta. Random matrices. The study of random matrice...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2010
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.82.051115