Moments of a single entry of circular orthogonal ensembles and Weingarten calculus

Consider a symmetric unitary random matrix $V=(v_{ij})_{1 \le i,j \le N}$ from a circular orthogonal ensemble. In this paper, we study moments of a single entry $v_{ij}$. For a diagonal entry $v_{ii}$ we give the explicit values of the moments, and for an off-diagonal entry $v_{ij}$ we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size $N$. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.Comment: 17 page

The Point of Origin of the Radio Radiation from the Unresolved Cores of Radio-Loud Quasars

Locating the exact point of origin of the core radiation in active galactic nuclei (AGN) would represent important progress in our understanding of physical processes in the central engine of these objects. However, due to our inability to resolve the region containing both the central compact object and the jet base, this has so far been difficult. Here, using an analysis in which the lack of resolution does not play a significant role, we demonstrate that it may be impossible even in most radio loud sources for more than a small percentage of the core radiation at radio wavelengths to come from the jet base. We find for 3C279 that $\sim85$ percent of the core flux at 15 GHz must come from a separate, reasonably stable, region that is not part of the jet base, and that then likely radiates at least quasi-isotropically and is centered on the black hole. The long-term stability of this component also suggests that it may originate in a region that extends over many Schwarzschild radii.Comment: 7 pages with 3 figures, accepted for publication in Astrophysics and Space Scienc

Symmetrized models of last passage percolation and non-intersecting lattice paths

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

The interaction of a gap with a free boundary in a two dimensional dimer system

Let $\ell$ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let \Cal H be the half plane to the left of $\ell$. We consider lozenge tilings of \Cal H that have a triangular gap of side-length two and in which $\ell$ is a free boundary - i.e., tiles are allowed to protrude out half-way across $\ell$. We prove that the correlation function of this gap near the free boundary has asymptotics $\frac{1}{4\pi r}$, $r\to\infty$, where $r$ is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te

From Vicious Walkers to TASEP

We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for $m$ particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For $m$ particles its asymptotic behavior is shown to be $e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty$ and $e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty$.Comment: 37 pages, 4 figures, Corrected reference

Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem

In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined

On absolute moments of characteristic polynomials of a certain class of complex random matrices

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.Comment: 41 page, typos correcte

Persistent Spin Currents in Helimagnets

We demonstrate that weak external magnetic fields generate dissipationless spin currents in the ground state of systems with spiral magnetic order. Our conclusions are based on phenomenological considerations and on microscopic mean-field theory calculations for an illustrative toy model. We speculate on possible applications of this effect in spintronic devices.Comment: 9 pages, 6 figures, updated version as published, Journal referenc

Influence of a Uniform Current on Collective Magnetization Dynamics in a Ferromagnetic Metal

We discuss the influence of a uniform current, $\vec{j}$, on the magnetization dynamics of a ferromagnetic metal. We find that the magnon energy $\epsilon(\vec{q})$ has a current-induced contribution proportional to $\vec{q}\cdot \vec{\cal J}$, where $\vec{\cal J}$ is the spin-current, and predict that collective dynamics will be more strongly damped at finite ${\vec j}$. We obtain similar results for models with and without local moment participation in the magnetic order. For transition metal ferromagnets, we estimate that the uniform magnetic state will be destabilized for $j \gtrsim 10^{9} {\rm A} {\rm cm}^{-2}$. We discuss the relationship of this effect to the spin-torque effects that alter magnetization dynamics in inhomogeneous magnetic systems.Comment: 12 pages, 2 figure

In-situ fluorescence spectroscopy indicates total bacterial abundance and dissolved organic carbon

We explore in-situ fluorescence spectroscopy as an instantaneous indicator of total bacterial abundance and faecal contamination in drinking water. Eighty-four samples were collected outside of the recharge season from groundwater-derived water sources in Dakar, Senegal. Samples were analysed for tryptophan-like (TLF) and humic-like (HLF) fluorescence in-situ, total bacterial cells by flow cytometry, and potential indicators of faecal contamination such as thermotolerant coliforms (TTCs), nitrate, and in a subset of 22 samples, dissolved organic carbon (DOC). Significant single-predictor linear regression models demonstrated that total bacterial cells were the most effective predictor of TLF, followed by on-site sanitation density; TTCs were not a significant predictor. An optimum multiple-predictor model of TLF incorporated total bacterial cells, nitrate, nitrite, on-site sanitation density, and sulphate (r2 0.68). HLF was similarly related to the same parameters as TLF, with total bacterial cells being the best correlated (ρs 0.64). In the subset of 22 sources, DOC clustered with TLF, HLF, and total bacterial cells, and a linear regression model demonstrated HLF was the best predictor of DOC (r2 0.84). The intergranular nature of the aquifer, timing of the study, and/or non-uniqueness of the signal to TTCs can explain the significant associations between TLF/HLF and indicators of faecal contamination such as on-site sanitation density and nutrients but not TTCs. The bacterial population that relates to TLF/HLF is likely to be a subsurface community that develops in-situ based on the availability of organic matter originating from faecal sources. In-situ fluorescence spectroscopy instantly indicates a drinking water source is impacted by faecal contamination but it remains unclear how that relates specifically to microbial risk in this setting