1. CJM Online first
 Handelman, David

Nearly approximate transitivity (AT) for circulant matrices
By previous work of Giordano and the author, ergodic
actions of $\mathbf Z$ (and other discrete groups) are completely classified
measuretheoretically by their dimension space, a construction
analogous to the dimension group used in C*algebras and topological
dynamics. Here we investigate how far from AT (approximately
transitive) can actions be which derive from circulant (and related)
matrices. It turns out not very: although nonAT actions can
arise from this method of construction, under very modest additional
conditions, ATness arises; in addition, if we drop the positivity
requirement in the isomorphism of dimension spaces, then all
these ergodic actions satisfy an analogue of AT. Many examples
are provided.
Keywords:approximately transitive, ergodic transformation, circulant matrix, hemicirculant matrix, dimension space, matrixvalued random walk Categories:37A05, 06F25, 28D05, 46B40, 60G50 

2. CJM Online first
 BenaychGeorges, Florent; Cébron, Guillaume; Rochet, Jean

Fluctuation of matrix entries and application to outliers of elliptic matrices
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in
K}$ which is invariant, in law, under unitary conjugation, we
give general sufficient conditions for central limit theorems
for random variables of the type $\operatorname{Tr}(\mathbf{A}_k
\mathbf{M})$, where the matrix $\mathbf{M}$ is deterministic
(such random variables include for example the normalized matrix
entries of the $\mathbf{A}_k$'s). A consequence is the asymptotic
independence of the projection of the matrices $\mathbf{A}_k$
onto the subspace of null trace matrices from their projections
onto the orthogonal of this subspace. These results are used
to study the asymptotic behavior of the outliers of a spiked
elliptic random matrix. More precisely, we show that the fluctuations
of these outliers around their limits can have various rates
of convergence, depending on the Jordan Canonical Form of the
additive perturbation. Also, some correlations can arise between
outliers at a macroscopic distance from each other. These phenomena
have already been observed
with random matrices
from the Single Ring Theorem.
Keywords:random matrix, Gaussian fluctuation, spiked model, elliptic random matrix, Weingarten calculus, Haar measure Categories:60B20, 15B52, 60F05, 46L54 

3. CJM 2016 (vol 68 pp. 1159)
 Yattselev, Maxim L.

Strong Asymptotics of HermitePadÃ© Approximants for Angelesco Systems
In this work type II HermitePadÃ© approximants for a vector
of Cauchy transforms of smooth Jacobitype densities are considered.
It is assumed that densities are supported on mutually disjoint
intervals (an Angelesco system with complex weights). The formulae
of strong asymptotics are derived for any ray sequence of multiindices.
Keywords:HermitePadÃ© approximation, multiple orthogonal polynomials, nonHermitian orthogonality, strong asymptotics, matrix RiemannHilbert approach Categories:42C05, 41A20, 41A21 

4. CJM 2012 (vol 65 pp. 1020)
 Goulden, I. P.; GuayPaquet, Mathieu; Novak, Jonathan

Monotone Hurwitz Numbers in Genus Zero
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers related to the expansion of complete symmetric functions in the JucysMurphy elements, and have arisen in recent work on the the asymptotic expansion of the HarishChandraItzyksonZuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone joincut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
Keywords:Hurwitz numbers, matrix models, enumerative geometry Categories:05A15, 14E20, 15B52 

5. CJM 2010 (vol 63 pp. 3)
 Banica, T.; Belinschi, S. T.; Capitaine, M.; Collins, B.

Free Bessel Laws
We introduce and study a remarkable family of real probability
measures $\pi_{st}$ that we call free Bessel laws. These are related
to the free Poisson law $\pi$ via the formulae
$\pi_{s1}=\pi^{\boxtimes s}$ and ${\pi_{1t}=\pi^{\boxplus t}}$. Our
study includes definition and basic properties, analytic aspects
(supports, atoms, densities), combinatorial aspects (functional
transforms, moments, partitions), and a discussion of the relation
with random matrices and quantum groups.
Keywords:Poisson law, Bessel function, Wishart matrix, quantum group Categories:46L54, 15A52, 16W30 

6. CJM 2010 (vol 62 pp. 758)
 Dolinar, Gregor; Kuzma, Bojan

General Preservers of QuasiCommutativity
Let ${ M}_n$ be the algebra of all $n \times n$ matrices over $\mathbb{C}$. We say that $A, B \in { M}_n$ quasicommute if there exists a nonzero $\xi \in \mathbb{C}$ such that $AB = \xi BA$. In the paper we classify bijective not necessarily linear maps $\Phi \colon M_n \to M_n$ which preserve quasicommutativity in both directions.
Keywords:general preservers, matrix algebra, quasicommutativity Categories:15A04, 15A27, 06A99 

7. CJM 2008 (vol 60 pp. 1050)
 Huang, Wenling; Semrl, Peter \v

Adjacency Preserving Maps on Hermitian Matrices
Hua's fundamental theorem of the geometry of hermitian matrices
characterizes bijective maps on the space of all $n\times n$
hermitian matrices preserving adjacency in both directions.
The problem of possible improvements
has been open for a while. There are three natural problems here.
Do we need the bijectivity assumption? Can we replace the
assumption of preserving adjacency in both directions by the
weaker assumption of preserving adjacency in one direction only?
Can we obtain such a characterization for maps acting between the
spaces of hermitian matrices of different sizes? We answer all
three questions for the complex hermitian matrices, thus obtaining
the optimal structural result for adjacency preserving maps on
hermitian matrices over the complex field.
Keywords:rank, adjacency preserving map, hermitian matrix, geometry of matrices Categories:15A03, 15A04, 15A57, 15A99 

8. CJM 2007 (vol 59 pp. 638)
 MacDonald, Gordon W.

Distance from Idempotents to Nilpotents
We give bounds on the distance from a nonzero idempotent to the
set of nilpotents in the set of $n\times n$ matrices in terms of
the norm of the idempotent. We construct explicit idempotents and
nilpotents which achieve these distances, and determine exact
distances in some special cases.
Keywords:operator, matrix, nilpotent, idempotent, projection Categories:47A15, 47D03, 15A30 

9. CJM 2004 (vol 56 pp. 776)
 Lim, Yongdo

Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices
We explicitly describe
the best approximation in
geodesic submanifolds of positive definite matrices
obtained from involutive
congruence transformations on the
CartanHadamard manifold ${\mathrm{Sym}}(n,{\Bbb R})^{++}$ of
positive definite matrices.
An explicit calculation for the minimal distance
function from the geodesic submanifold
${\mathrm{Sym}}(p,{\mathbb R})^{++}\times
{\mathrm{Sym}}(q,{\mathbb R})^{++}$ block diagonally embedded in
${\mathrm{Sym}}(n,{\mathbb R})^{++}$ is
given in terms of metric and
spectral geometric means, Cayley transform, and Schur
complements of positive definite matrices when $p\leq 2$ or $q\leq 2.$
Keywords:Matrix approximation, positive, definite matrix, geodesic submanifold, CartanHadamard manifold,, best approximation, minimal distance function, global tubular, neighborhood theorem, Schur complement, metric and spectral, geometric mean, Cayley transform Categories:15A48, 49R50, 15A18, 53C3 

10. CJM 2003 (vol 55 pp. 91)
 Choi, ManDuen; Li, ChiKwong; Poon, YiuTung

Some Convexity Features Associated with Unitary Orbits
Let $\mathcal{H}_n$ be the real linear space of $n\times n$ complex
Hermitian matrices. The unitary (similarity) orbit $\mathcal{U}
(C)$ of $C \in \mathcal{H}_n$ is the collection of all matrices
unitarily similar to $C$. We characterize those $C \in \mathcal{H}_n$
such that every matrix in the convex hull of $\mathcal{U}(C)$ can
be written as the average of two matrices in $\mathcal{U}(C)$. The
result is used to study spectral properties of submatrices of
matrices in $\mathcal{U}(C)$, the convexity of images of $\mathcal{U}
(C)$ under linear transformations, and some related questions
concerning the joint $C$numerical range of Hermitian matrices.
Analogous results on real symmetric matrices are also discussed.
Keywords:Hermitian matrix, unitary orbit, eigenvalue, joint numerical range Categories:15A60, 15A42 
