ترغب بنشر مسار تعليمي؟ اضغط هنا

Freeness and The Partial Transposes of Wishart Random Matrices

84   0   0.0 ( 0 )
 نشر من قبل James A. Mingo
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف James A. Mingo




اسأل ChatGPT حول البحث

We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives a example where the partial transpose produces freeness at the operator level. Finally we investigate the case of real Wishart matrices.

قيم البحث

اقرأ أيضاً

221 - Weihua Liu 2018
We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of the matrices, are operator valued semicircular laws. Furthermore, we prove an operator valued analogue of Voiculescus asymptotic freeness theorem. By replacing conditional independence with Boolean independence, we show that the limit laws of the random matrices are Operator-valued Bernoulli laws.
We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and Thorbjornsen where GU E matrices are considered, as well as the classical asymptotic freeness for Wigner matrices (i.e. convergence of the moments) proved by Dykema. We also study the Wishart case.
93 - F. Hiai , D. Petz 2005
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 infinity. The result is formulated on the tracial state space $TS({cal A})$ of the universal $C^*$-algebra ${cal A}$ generated by two selfadjoint projections. The random pair $(P(N),Q(N))$ determines a random tracial state $tau_N in TS({cal A})$ and $tau_N$ satisfies the large deviation. The rate function is in close connection with Voiculescus free entropy defined for pairs of projections.
244 - Adam Dor-On 2021
We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent ratios of tr ansition probabilities. These C*-algebras give rise to new notions of ratio limit space and boundary for such random walks, which are computed by appealing to a companion paper by Woess. Our combined results are leveraged to identify a unique symmetry-equivariant quotient C*-algebra for any symmetric random walk on a hyperbolic group, shedding light on a question of Viselter on C*-algebras of subproduct systems.
Let $Q_{n,d}$ denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at random from the subset of vectors in ${0,1}^n$ having precisely $d$ entries equal to $1$. We present a short proof of the fact that $Pr[det(Q_{n,d})=0] = Oleft(frac{n^{1/2}log^{3/2} n}{d}right)=o(1)$, whenever $d=omega(n^{1/2}log^{3/2} n)$. In particular, our proof accommodates sparse random combinatorial matrices in the sense that $d = o(n)$ is allowed. We also consider the singularity of deterministic integer matrices $A$ randomly perturbed by a sparse combinatorial matrix. In particular, we prove that $Pr[det(A+Q_{n,d})=0]=Oleft(frac{n^{1/2}log^{3/2} n}{d}right)$, again, whenever $d=omega(n^{1/2}log^{3/2} n)$ and $A$ has the property that $(1,-d)$ is not an eigenpair of $A$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا