Random words, quantum statistics, central limits, random matrices
نویسندگان
چکیده
منابع مشابه
Random words, quantum statistics, central limits, random matrices
Recently Tracy and Widom conjectured [25] and Johansson proved [13] that the expected shape λ of the semi-standard tableau produced by a random word in k letters is asymptotically the spectrum of a random traceless k × k GUE matrix. In this article we give two arguments for this fact. In the first argument, we realize the random matrix itself as a quantum random variable on the space of random ...
متن کاملEigenvector Statistics of Sparse Random Matrices
We prove that the bulk eigenvectors of sparse random matrices, i.e. the adjacency matrices of ErdősRényi graphs or random regular graphs, are asymptotically jointly normal, provided the averaged degree increases with the size of the graphs. Our methodology follows [6] by analyzing the eigenvector flow under Dyson Brownian motion, combining with an isotropic local law for Green’s function. As an...
متن کاملRandom numbers and random matrices: Quantum chaos meets number theory
The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the ei...
متن کاملCentral Limits and Homogenization in Random Media
We consider the perturbation of elliptic pseudo-differential operators P (x,D) with more than square integrable Green’s functions by random, rapidly varying, sufficiently mixing, potentials of the form q( ε , ω). We analyze the source and spectral problems associated to such operators and show that the rescaled difference between the perturbed and unperturbed solutions may be written asymptotic...
متن کاملWeak limits for quantum random walks.
We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X(n) denoting position at time n, we show that X(n)/n converges weakly as n--> infinity to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain precedi...
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: Methods and Applications of Analysis
سال: 2002
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2002.v9.n1.a3