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

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

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

Evaluating the function of wildcat faecal marks in relation to the defence of favourable hunting areas

This is an Accepted Manuscript of an article published by Taylor & Francis in Ethology Ecology and Evolution on 2015, available online: http://www.tandfonline.com/10.1080/03949370.2014.905499To date, there have been no studies of carnivores that have been specifically designed to examine the function of scent marks in trophic resource defence, although several chemical communication studies have discussed other functions of these marks. The aim of this study was to test the hypothesis that faecal marks deposited by wildcats (Felis silvestris) serve to defend their primary trophic resource, small mammals. Field data were collected over a 2-year period in a protected area in northwestern Spain. To determine the small mammal abundance in different habitat types, a seasonal live trapping campaign was undertaken in deciduous forests, mature pine forests and scrublands. In each habitat, we trapped in three widely separated Universal Transverse Mercator (UTM) cells. At the same time that the trapping was being performed, transects were conducted on foot along forest roads in each trapping cell and in one adjacent cell to detect fresh wildcat scats that did or did not have a scent-marking function. A scat was considered to have a presumed marking function when it was located on a conspicuous substrate, above ground level, at a crossroad or in a latrine. The number of faecal marks and the small mammal abundance varied by habitat type but not by seasons. The results of the analysis of covariance (ANCOVA) indicated that small mammal abundance and habitat type were the factors that explained the largest degrees of variation in the faecal marking index (number of faecal marks in each cell/number of kilometres surveyed in each cell). This result suggests that wildcats defended favourable hunting areas. They mark most often where their main prey lives and so where they spend the most time hunting (in areas where their main prey is more abundant). This practice would allow wildcats to protect their main trophic resource and would reduce intraspecific trophic competitio

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