138 research outputs found

### Free probability aspect of irreducible meander systems, and some related observations about meanders

We consider the concept of irreducible meandric system introduced by Lando
and Zvonkin. We place this concept in the lattice framework of NC(n). As a
consequence, we show that the even generating function for irreducible meandric
systems is the R-transform of XY, where X and Y are classically (commuting)
independent random variables, and each of X,Y has centred semicircular
distribution of variance 1. Following this point of view, we make some
observations about the symmetric linear functional on polynomials which has
R-transform given by the even generating function for meanders.Comment: Two new remarks in Sections 3 and 5, and an additional referenc

### Multi-variable subordination distributions for free additive convolution

Let k be a positive integer and let D_k denote the space of joint
distributions for k-tuples of selfadjoint elements in C*-probability space. The
paper studies the concept of "subordination distribution of \mu \boxplus \nu
with respect to \nu" for \mu, \nu \in D_k, where \boxplus is the operation of
free additive convolution on D_k. The main tools used in this study are
combinatorial properties of R-transforms for joint distributions and a related
operator model, with operators acting on the full Fock space
Multi-variable subordination turns out to have nice relations to a process of
evolution towards \boxplus-infinite divisibility on D_k that was recently found
by Belinschi and Nica (arXiv:0711.3787). Most notably, one gets better insight
into a connection which this process was known to have with free Brownian
motion.Comment: Minor modifications and reference added to 1st version. 34 pages, no
figure

### Posets of annular non-crossing partitions of types B and D

We study the set \sncb (p,q) of annular non-crossing permutations of type
B, and we introduce a corresponding set \ncb (p,q) of annular non-crossing
partitions of type B, where $p$ and $q$ are two positive integers. We prove
that the natural bijection between \sncb (p,q) and \ncb (p,q) is a poset
isomorphism, where the partial order on \sncb (p,q) is induced from the
hyperoctahedral group $B_{p+q}$, while \ncb (p,q) is partially ordered by
reverse refinement. In the case when $q=1$, we prove that \ncb (p,1) is a
lattice with respect to reverse refinement order.
We point out that an analogous development can be pursued in type D, where
one gets a canonical isomorphism between \sncd (p,q) and \ncd (p,q). For
$q=1$, the poset \ncd (p,1) coincides with a poset ``$NC^{(D)} (p+1)$''
constructed in a paper by Athanasiadis and Reiner in 2004, and is a lattice by
the results of that paper.Comment: Revised version (shortened Introduction, corrected typos), 31 pages,
4 figures, to appear in Discrete Mathematic

### Double-ended queues and joint moments of left-right canonical operators on full Fock space

We follow the guiding line offered by canonical operators on the full Fock
space, in order to identify what kind of cumulant functionals should be
considered for the concept of bi-free independence introduced in the recent
work of Voiculescu. By following this guiding line we arrive to consider, for a
general noncommutative probability space (A, phi), a family of "(l,r)-cumulant
functionals" which enlarges the family of free cumulant functionals of the
space. In the motivating case of canonical operators on the full Fock space we
find a simple formula for a relevant family of (l,r)-cumulants of a (2d)-tuple
(A_1, ..., A_d, B_1, ..., B_d), with A_1, ... , A_d canonical operators on the
left and B_1, ... , B_d canonical operators on the right. This extends a known
one-sided formula for free cumulants of A_1, ..., A_d, which establishes a
basic operator model for the R-transform of free probability.Comment: In this (final) version, the introduction was re-written to better
show the motivation for the question considered in the pape

### Infinitesimal non-crossing cumulants and free probability of type B

Free probabilistic considerations of type B first appeared in a paper by
Biane, Goodman and Nica in 2003. Recently, connections between type B and
infinitesimal free probability were put into evidence by Belinschi and
Shlyakhtenko (arXiv:0903.2721). The interplay between "type B" and
"infinitesimal" is also the object of the present paper. We study infinitesimal
freeness for a family of unital subalgebras A_1, ..., A_k in an infinitesimal
noncommutative probability space (A, phi, phi'), and we introduce a concept of
infinitesimal non-crossing cumulant functionals for (A, phi, phi'), obtained by
taking a formal derivative in the formula for usual non-crossing cumulants. We
prove that the infinitesimal freeness of A_1, ... A_k is equivalent to a
vanishing condition for mixed cumulants; this gives the infinitesimal
counterpart for a theorem of Speicher from "usual" free probability. We show
that the lattices of non-crossing partitions of type B appear in the
combinatorial study of (A, phi, phi'), in the formulas for infinitesimal
cumulants and when describing alternating products of infinitesimally free
random variables. As an application of alternating free products, we observe
the infinitesimal analogue for the well-known fact that freeness is preserved
under compression with a free projection. As another application, we observe
the infinitesimal analogue for a well-known procedure used to construct free
families of free Poisson elements. Finally, we discuss situations when the
freeness of A_1, ..., A_k in (A, phi) can be naturally upgraded to
infinitesimal freeness in (A, phi, phi'), for a suitable choice of a "companion
functional" phi'.Comment: 38 pages, 1 figur

### PUBLIC POLICIES IN THE BUCHAREST METROPOLITAN AREA â INERTIAS AND CHALLENGES FOR LOCAL ADMINISTATION

Bucharest, the most developed city from Romania, covers perhaps most superlatives in any field for describing its importance in the national territory. This city is the only European capital without having an integrated and coherent urban policy adopted by the state. There are the short term local interventions of adjusting trend, specific to Romania, that donât rely on general directions of territorial development, because they are neither intended nor assumed by the competent decisional authorities. In general, the problem is lack of partnership between the project elaborating actors and the implementing actors of those projects. Bucharest municipality has important potential reserves, but the general status is far from corresponding to the demands recommended by the European development policy. The loss of potential, as a result of the decision of modernization postponements, produces both immediate negative effects, and also induces vast losses on a medium and long term. It requires greater costs, with resonance in the entire economic system and in the living conditions of the area. In present study, we try to evaluate the public policies regarding the Metropolitan Area of Bucharest which should be centered on 2 main issues â territorial cohesion and polycentric policy. Because of the difficulties of their understanding by the politicians and thus, the slowness of their use, the evaluation made by us is using a qualitative approach. Our conclusions drift from the result of the efforts made by the CPUMB for convincing the politicians of using and implementing the results drawn by researches and studies made.Bucharest Metropolitan Area (BMA), public policies, territorial cohesion, polycentricity

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