Let (A, ϕ) be a C ∗ -probability space – by which we mean that A is a unital C ∗-algebra and ϕ is a state of A (ϕ : A → C positive linear functional, such that ϕ(I ) = 1).
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
The number variance of the critical chiral random matrix model shows a linear Ldependence for a large L (in units of the average level spacing) whereas it coincides with the chGUE result for small values of L.
Chiral Random Matrix Model for Critical Statistics
We consider F-linear tensor categories C with simple unit and ﬁnitely many isomorphism classes of simple ob jects.
From Subfactors to Categories and Topology II. The quantum double of tensor categories and subfactors
Theorem 5.21 Let ρ an unital linear map from A to A, with curvature ωρ .
Coassociativity breaking and oriented graphs
Theorem B) to polynomials (resp. linear combinations) with coeﬃcients in an arbitrary unital exact C ∗ algebra.
A new application of Random Matrices: Ext(C*_{red}(F_2)) is not a group
The Lie algebra G∗ = SL(n, R) is then the set of n × n real matrices of zero trace, and generates the linear group of transformations represented by real n × n matrices of unit determinant.
Random matrix theory and symmetric spaces
For the Toeplitz and Hankel cases, with each partition word w we associate a system of linear equations which determine the cross section of the unit hypercube, and deﬁne the corresponding volume p(w).
Spectral measure of large random Hankel, Markov and Toeplitz matrices
The last relation expresses that, modulo a phase factor, the states of the new basis are equivalent upon a shift of their momenta p in any linear combination with integer coeﬃcients of half the unit cell vectors of the reciprocal lattice corresponding to the periodicity of the density.
Anlaytic mean-field Hall crystal solution at nu=1/3: composite fermion like sub-bands and correlation effects
Let G be a ﬁnite subset of A, δ > 0 and L : A → B be a G -δ -multiplicative contractive completely positive linear map, where B is a unital C ∗ -algebra.
Simple nuclear $C^*$-algebras of tracial topological rank one
Rn is n-dimensional linear space over reals, and Sn is a (n − 1)-dimensional unit simplex in Rn , Sn = {x ∈ Rn | xi ≥ 0 and Pi xi = 1}.
Grade of Membership Analysis: One Possible Approach to Foundations
Asa denote the set of self-adjoint elements of A. A C ∗ -algebra (A, ∗) is said unital if it contains a neutral element denoted I . A can always be realized as a sub-C ∗ -algebra of the space B (H ) of bounded linear operators on a Hilbert space H .
Large deviations and stochastic calculus for large random matrices
Note also that if X and Y are aﬃliated with A, aX + bY is also aﬃliated with A for any a, b ∈ R. A state τ on a unital von Neumann algebra (A, ∗) is a linear form on A such that τ (Asa ) ⊂ R and 1.
Large deviations and stochastic calculus for large random matrices
We ﬁx a tracial non-commutative ∗-probability space (A, ϕ); i. e., A is a unital ∗-algebra and ϕ : A → C is a unital tracial positive linear functional.
Asymptotic Freeness of Random Permutation Matrices from Gaussian Matrices
Dayantis et al. carried out simulations of free chains (random-ﬂight walks) conﬁned to cubes of various linear dimensions 6 − 20, in units of the lattice constant.
Localization of Polymers in Random Media: Analogy with Quantum Particles in Disorder
In Racine has determined the maximal (unital) subalgebras of ﬁnitedimensional special simple linear Jordan algebras.
Simple decompositions of the exceptional Jordan algebra
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