792 research outputs found
Asymptotics of Selberg-like integrals by lattice path counting
We obtain explicit expressions for positive integer moments of the
probability density of eigenvalues of the Jacobi and Laguerre random matrix
ensembles, in the asymptotic regime of large dimension. These densities are
closely related to the Selberg and Selberg-like multidimensional integrals. Our
method of solution is combinatorial: it consists in the enumeration of certain
classes of lattice paths associated to the solution of recurrence relations
Rectangular Matrix Models and Combinatorics of Colored Graphs
We present applications of rectangular matrix models to various combinatorial
problems, among which the enumeration of face-bicolored graphs with prescribed
vertex degrees, and vertex-tricolored triangulations. We also mention possible
applications to Interaction-Round-a-Face and hard-particle statistical models
defined on random lattices.Comment: 42 pages, 11 figures, tex, harvmac, eps
Characteristic polynomials of complex random matrix models
We calculate the expectation value of an arbitrary product of characteristic polynomials of
complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials
in the complex plane our result can be written in terms of a determinant containing these
polynomials and their kernel. It generalizes the known expression for hermitian matrices and it
also provides a generalization of the Christoffel formula to the complex plane. The derivation we
present holds for complex matrix models with a general weight function at finite-N, where N is the
size of the matrix. We give some explicit examples at finite-N for specific weight functions. The
characteristic polynomials in the large-N limit at weak and strong non-hermiticity follow easily
and they are universal in the weak limit. We also comment on the issue of the BMN large-N limit
Breakdown of Universality in Random Matrix Models
We calculate smoothed correlators for a large random matrix model with a
potential containing products of two traces \tr W_1(M) \cdot \tr W_2(M) in
addition to a single trace \tr V(M). Connected correlation function of
density eigenvalues receives corrections besides the universal part derived by
Brezin and Zee and it is no longer universal in a strong sense.Comment: 16 pages, LaTex, references and footnote adde
Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules
The minimal theories are labelled by a Lie algebra pair where
is of -- type. For these theories on a cylinder we conjecture a
complete set of conformal boundary conditions labelled by the nodes of the
tensor product graph . The cylinder partition functions are given
by fusion rules arising from the graph fusion algebra of . We
further conjecture that, for each conformal boundary condition, an integrable
boundary condition exists as a solution of the boundary Yang-Baxter equation
for the associated lattice model. The theory is illustrated using the
or 3-state Potts model.Comment: 4 pages, REVTe
Morphological and moisture availability controls of the leaf area-to-sapwood area ratio: Analysis of measurements on Australian trees
© 2015 Published by John Wiley & Sons Ltd. The leaf area-to-sapwood area ratio (LA:SA) is a key plant trait that links photosynthesis to transpiration. The pipe model theory states that the sapwood cross-sectional area of a stem or branch at any point should scale isometrically with the area of leaves distal to that point. Optimization theory further suggests that LA:SA should decrease toward drier climates. Although acclimation of LA:SA to climate has been reported within species, much less is known about the scaling of this trait with climate among species. We compiled LA:SA measurements from 184 species of Australian evergreen angiosperm trees. The pipe model was broadly confirmed, based on measurements on branches and trunks of trees from one to 27 years old. Despite considerable scatter in LA:SA among species, quantile regression showed strong (0.2 < R1 < 0.65) positive relationships between two climatic moisture indices and the lowermost (5%) and uppermost (5-15%) quantiles of log LA:SA, suggesting that moisture availability constrains the envelope of minimum and maximum values of LA:SA typical for any given climate. Interspecific differences in plant hydraulic conductivity are probably responsible for the large scatter of values in the mid-quantile range and may be an important determinant of tree morphology. We compiled LA:SA measurements from 183 species of Australian evergreen angiosperm trees. The pipe model was broadly confirmed. LA:SA quantile regression showed positive relationships between two climatic moisture indices and the lowermost and uppermost quantiles
Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
We consider sl(2) minimal conformal field theories and the dual parafermion
models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS)
models and its Virasoro modules expressed in terms of paths, we propose a
general level-by-level algorithm to build matrix representations of the
Virasoro generators and chiral vertex operators (CVOs). We implement our scheme
for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories
on a cylinder and confirm that it is consistent with the known two-point
functions for the CVOs and energy-momentum tensor. Our algorithm employs a
distinguished basis which we call the L_1-basis. We relate the states of this
canonical basis level-by-level to orthonormalized Virasoro states
Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity
The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we establish the universality of the asymptotics of orthogonal polynomials in the complex plane. The universality of the correlation functions then follows from that of the kernel of orthogonal polynomials and a mapping of massive to massless correlators
Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
By using the method of orthogonal polynomials we analyze the statistical
properties of complex eigenvalues of random matrices describing a crossover
from Hermitian matrices characterized by the Wigner- Dyson statistics of real
eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were
studied by Ginibre.
Two-point statistical measures (as e.g. spectral form factor, number variance
and small distance behavior of the nearest neighbor distance distribution
) are studied in more detail. In particular, we found that the latter
function may exhibit unusual behavior for some parameter
values.Comment: 4 pages, RevTE
Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
This is the second of two articles (independent of each other) devoted to the
analysis of the path description of the states in su(2)_k WZW models. Here we
present a constructive derivation of the fermionic character at level k based
on these paths. The starting point is the expression of a path in terms of a
sequence of nonlocal (formal) operators acting on the vacuum ground-state path.
Within this framework, the key step is the construction of the level-k operator
sequences out of those at level-1 by the action of a new type of operators.
These actions of operators on operators turn out to have a path interpretation:
these paths are precisely the finitized RSOS paths related to the unitary
minimal models M(k+1,k+2). We thus unravel -- at the level of the path
representation of the states --, a direct factorization into a k=1 spinon part
times a RSOS factor. It is also pointed out that since there are two fermionic
forms describing these finite RSOS paths, the resulting fermionic su(2)_k
characters arise in two versions. Finally, the relation between the present
construction and the Nagoya spectral decomposition of the path space is
sketched.Comment: 28 page
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