65 research outputs found
Eigenvalue density of Wilson loops in 2D SU(N) YM
In 1981 Durhuus and Olesen (DO) showed that at infinite N the eigenvalue
density of a Wilson loop matrix W associated with a simple loop in
two-dimensional Euclidean SU(N) Yang-Mills theory undergoes a phase transition
at a critical size. The averages of det(z-W), 1/det(z-W), and det(1+uW)/(1-vW)
at finite N lead to three different smoothed out expressions, all tending to
the DO singular result at infinite N. These smooth extensions are obtained and
compared to each other.Comment: 35 pages, 8 figure
Numerical semigroups with large embedding dimension satisfy Wilf's conjecture
We give an affirmative answer to Wilf's conjecture for numerical semigroups
satisfying 2 \nu \geq m, where \nu and m are respectively the embedding
dimension and the multiplicity of a semigroup. The conjecture is also proved
when m \leq 8 and when the semigroup is generated by a generalized arithmetic
sequence.Comment: 13 page
Dobiński relations and ordering of boson operators
We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations
On WZ-pairs which prove Ramanujan series
The known WZ-proofs for Ramanujan-type series related to gave us the
insight to develop a new proof strategy based on the WZ-method. Using this
approach we are able to find more generalizations and discover first WZ-proofs
for certain series of this type.Comment: 12 pages (preprint) + 1 page (addendum). The addendum (A Maple
program) is not in the Journal referenc
The smallest eigenvalue of Hankel matrices
Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive
measure with moments of any order. We study the large N behaviour of the
smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential
decay to zero for any measure with compact support. For general determinate
moment problems the decay to 0 of lambda_N can be arbitrarily slow or
arbitrarily fast. In the indeterminate case, where lambda_N is known to be
bounded below by a positive constant, we prove that the limit of the n'th
smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity
with n. The special case of the Stieltjes-Wigert polynomials is discussed
Condensing Momentum Modes in 2-d 0A String Theory with Flux
We use a combination of conformal perturbation theory techniques and matrix
model results to study the effects of perturbing by momentum modes two
dimensional type 0A strings with non-vanishing Ramond-Ramond (RR) flux. In the
limit of large RR flux (equivalently, mu=0) we find an explicit analytic form
of the genus zero partition function in terms of the RR flux and the
momentum modes coupling constant alpha. The analyticity of the partition
function enables us to go beyond the perturbative regime and, for alpha>> q,
obtain the partition function in a background corresponding to the momentum
modes condensation. For momenta such that 0<p<2 we find no obstruction to
condensing the momentum modes in the phase diagram of the partition function.Comment: 22 page
Condensation in nongeneric trees
We study nongeneric planar trees and prove the existence of a Gibbs measure
on infinite trees obtained as a weak limit of the finite volume measures. It is
shown that in the infinite volume limit there arises exactly one vertex of
infinite degree and the rest of the tree is distributed like a subcritical
Galton-Watson tree with mean offspring probability . We calculate the rate
of divergence of the degree of the highest order vertex of finite trees in the
thermodynamic limit and show it goes like where is the size of the
tree. These trees have infinite spectral dimension with probability one but the
spectral dimension calculated from the ensemble average of the generating
function for return probabilities is given by if the weight
of a vertex of degree is asymptotic to .Comment: 57 pages, 14 figures. Minor change
Concerning Order and Disorder in the Ensemble of Cu-O Chain Fragments in Oxygen Deficient Planes of Y-Ba-Cu-O
In connection with numerous X-ray and neutron investigations of some high
temperature superconductors (YBaCuO and related compounds) a
non-trivial part of the structure factor, coming from partly disordered
Cu-O--O-Cu chain fragments, situated within basal planes, CuO, can
be a subject of theoretical interest. Closely connected to such a diffusive
part of the structure factor are the correlation lengths, which are also
available in neutron and X-ray diffraction studies and depend on a degree of
oxygen disorder in a basal plane. The quantitative measure of such a disorder
can be associated with temperature of a sample anneal, , at which oxygen
in a basal plane remains frozen-in high temperature equilibrium after a fast
quench of a sample to room or lower temperature. The structure factor evolution
with is vizualized in figures after the numerical calculations. The
theoretical approach employed in the paper has been developed for the
orthorhombic state of YBCO.Comment: Revtex, 27 pages, 14 PostScript figures upon request, ITP/GU/94/0
Nash Equilibria in Discrete Routing Games with Convex Latency Functions
In a discrete routing game, each of n selfish users employs a mixed strategy to ship her (unsplittable) traffic over m parallel links. The (expected) latency on a link is determined by an arbitrary non-decreasing, non-constant and convex latency function φ. In a Nash equilibrium, each user alone is minimizing her (Expected) Individual Cost, which is the (expected) latency on the link she chooses. To evaluate Nash equilibria, we formulate Social Cost as the sum of the users ’ (Expected) Individual Costs. The Price of Anarchy is the worst-case ratio of Social Cost for a Nash equilibrium over the least possible Social Cost. A Nash equilibrium is pure if each user deterministically chooses a single link; a Nash equilibrium is fully mixed if each user chooses each link with non-zero probability. We obtain: For the case of identical users, the Social Cost of any Nash equilibrium is no more than the Social Cost of the fully mixed Nash equilibrium, which may exist only uniquely. Moreover, instances admitting a fully mixed Nash equilibrium enjoy an efficient characterization. For the case of identical users, we derive two upper bounds on the Price of Anarchy: For the case of identical links with a monomial latency function φ(x) = x d, the Price of Anarchy is the Bell number of order d + 1. For pure Nash equilibria, a generic upper bound from the Wardrop model can be transfered to discrete routing games. For polynomial latency functions with non-negative coefficients and degree d, this yields an upper bound of d + 1. For th
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
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