Explicit multi-matrix topological expansion for quaternionic random matrices
نویسندگان
چکیده
منابع مشابه
Right Eigenvalues for Quaternionic Matrices: a Topological Approach
We apply the Lefschetz Fixed Point Theorem to show that every square matrix over the quaternions has right eigenvalues. We classify them and discuss some of their properties such as an analogue of Jordan canonical form and diagonalization of elements of the compact symplectic group Sp(n).
متن کاملRandom right eigenvalues of Gaussian quaternionic matrices
We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance 1/n. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension n goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on mo...
متن کاملDuality of Real and Quaternionic Random Matrices
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner and Wishart families of random matrices the result gives the duality between moments of these families and the corresponding real Wigner and Wishart families.
متن کاملTopological Expansion in the Cubic Random Matrix Model
In this paper, we study the topological expansion in the cubic random matrix model, and we evaluate explicitly the expansion coefficients for genus 0 and 1. For genus 0 our formula coincides with the one in [6]. For higher genus, we obtain the asymptotic behavior of the coefficients in the expansion as the number of vertices of the associated graphs tends to infinity. Our study is based on the ...
متن کاملTopological expansion of the chain of matrices
We solve the loop equations to all orders in 1/N, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular prope...
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: Journal of Mathematical Physics
سال: 2016
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4940338