Large Deviations for Functions of Two Random Projection Matrices
نویسنده
چکیده
In this paper two independent and unitarily invariant projection matrices P (N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomials of them as the matrix size N converges to in nity. The result is formulated on the tracial state space TS(A) of the universal C -algebra A generated by two selfadjoint projections. The random pair (P (N); Q(N)) determines a random tracial state N 2 TS(A) and N satis es the large deviation. The rate function is in close connection with Voiculescu's free entropy de ned for pairs of projections. Mathematics Subject Classi cation: 15A52, 60F10, 46L54.
منابع مشابه
Large deviations and stochastic calculus for large random matrices
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they attracted lots of interests, in particular due to a serie of mathematical breakthroughs allowing for instance a better understanding of local properties of their s...
متن کاملLarge deviations for random matricial moment problems
We consider the moment space Mn corresponding to p × p complex matrix measures defined on K (K = [0, 1] or K = T). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when n→∞. First we fix an integer k and study the vector of the first k components of a random element ofMn . We obtain a LDP in the set of k-arrays of p× p matrices. Then we lift ...
متن کاملLARGE DEVIATIONS FOR RANDOM PROJECTIONS OF `p BALLS BY NINA GANTERT∗ , STEVEN
Let p∈ [1,∞]. Consider the projection of a uniform random vector from a suitably normalized `p ball in Rn onto an independent random vector from the unit sphere. We show that sequences of such random projections, when suitably normalized, satisfy a large deviation principle (LDP) as the dimension n goes to ∞, which can be viewed as an annealed LDP. We also establish a quenched LDP (conditioned ...
متن کاملComputing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...
متن کاملModeling of Infinite Divisible Distributions Using Invariant and Equivariant Functions
Basu’s theorem is one of the most elegant results of classical statistics. Succinctly put, the theorem says: if T is a complete sufficient statistic for a family of probability measures, and V is an ancillary statistic, then T and V are independent. A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics. In addition ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005