Quantum invariant families of matrices in free probability

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

R-cyclic families of matrices in free probability

We introduce the concept of “R-cyclic family” of matrices with entries in a noncommutative probability space; the definition consists in asking that only the “cyclic” non-crossing cumulants of the entries of the matrices are allowed to be non-zero. Let A1, . . . , As be an R-cyclic family of d×d matrices over a non-commutative probability space (A, φ). We prove a convolution-type formula for th...

متن کامل

Free probability and random matrices

In these lectures notes we will present and focus on free probability as a tool box to study the spectrum of polynomials in several (eventually) random matrices, and provide some applications.

متن کامل

Multiuser Receivers, Random Matrices and Free Probability

There are often curious and deep connections between engineering and mathematics. We tell one such story here. It starts with the engineering problem of capacity analysis of directsequence spread spectrum wireless networks. Using results from convergence of spectra of large random matrices, we obtain simple answers for a basic model of this problem, in terms of notions of effective bandwidths a...

متن کامل

Free Probability Theory and Random Matrices

Free probability theory originated in the context of operator algebras, however, one of the main features of that theory is its connection with random matrices. Indeed, free probability can be considered as the theory providing concepts and notations, without relying on random matrices, for dealing with the limit N → ∞ of N ×N -random matrices. One of the basic approaches to free probability, o...

متن کامل

1 Winding - Invariant Prime Ideals in Quantum 3 × 3 Matrices

A complete determination of the prime ideals invariant under winding automorphisms in the generic 3 × 3 quantum matrix algebra Oq(M3(k)) is obtained. Explicit generating sets consisting of quantum minors are given for all of these primes, thus verifying a general conjecture in the 3 × 3 case. The result relies heavily on certain tensor product decompositions for winding-invariant prime ideals, ...

متن کامل

ذخیره 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 Functional Analysis

سال: 2011

ISSN: 0022-1236

DOI: 10.1016/j.jfa.2011.04.004