Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its mean (thus obtaining an asymptotically Gaussian distribution), we calculate the full distribution, including its tails which strongly deviate from the Gaussian behavior near the mean. The resulting distribution interpolates seamlessly between the Gaussian approximation for rates $R$ close to the ergodic value of the mutual information and the approach of Zheng and Tse for large signal to noise ratios $\rho$. This calculation provides us with a tool to obtain outage probabilities analytically at any point in the $(R, \rho, N)$ parameter space, as long as the number of antennas $N$ is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities, and it depends on the values of $R$ and $\rho$.Comment: Accepted for publication, IEEE Transactions on Information Theory (2010). Part of this work appears in the Proc. IEEE Information Theory Workshop, June 2009, Volos, Greec

Duality walls, duality trees and fractional branes

We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at which the number of degrees of freedom becomes infinite, and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory

Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schroedinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of the information transmission through non-linear optical fibers.Comment: 5 pages, 1 figur

A New Infinite Class of Quiver Gauge Theories

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadratic irrational numbers. The metrics for these manifolds still remain unknown.Comment: 29 pages, JHE

Entrepreneurial sons, patriarchy and the Colonels' experiment in Thessaly, rural Greece

Existing studies within the field of institutional entrepreneurship explore how entrepreneurs influence change in economic institutions. This paper turns the attention of scholarly inquiry on the antecedents of deinstitutionalization and more specifically, the influence of entrepreneurship in shaping social institutions such as patriarchy. The paper draws from the findings of ethnographic work in two Greek lowland village communities during the military Dictatorship (1967–1974). Paradoxically this era associated with the spread of mechanization, cheap credit, revaluation of labour and clear means-ends relations, signalled entrepreneurial sons’ individuated dissent and activism who were now able to question the Patriarch’s authority, recognize opportunities and act as unintentional agents of deinstitutionalization. A ‘different’ model of institutional change is presented here, where politics intersects with entrepreneurs, in changing social institutions. This model discusses the external drivers of institutional atrophy and how handling dissensus (and its varieties over historical time) is instrumental in enabling institutional entrepreneurship

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive nonlinear Schrödinger equation with a Gaussian random pulse as an initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through nonlinear optical fibers. © 2008 The American Physical Society

SINR statistics of correlated MIMO linear receivers

Linear receivers offer a low complexity option for multiantenna communication systems. Therefore, understanding the outage behavior of the corresponding SINR is important in a fading mobile environment. In this paper, we introduce a large deviation method, valid nominally for a large number $M$ of antennas, which provides the probability density of the SINR of Gaussian channel MIMO minimum mean square error (MMSE) and zero-forcing (ZF) receivers, with arbitrary transmission power profiles and in the presence of receiver antenna correlations. This approach extends the Gaussian approximation of the SINR, valid for large $M$ asymptotically close to the center of the distribution, to obtain the non-Gaussian tails of the distribution. Our methodology allows us to calculate the SINR distribution to next-to-leading order ($O(1/M)$) and showcase the deviations from approximations that have appeared in the literature (e.g., the Gaussian or the generalized Gamma distribution). We also analytically evaluate the outage probability, as well as the uncoded bit-error-rate. We find that our approximation is quite accurate even for the smallest antenna arrays (2$\,\times\,$ 2). © 1963-2012 IEEE

Living at the edge: A large deviations approach to the outage MIMO capacity

A large deviations approach is introduced, which calculates the probability density and outage probability of the multiple-input multiple-output (MIMO) mutual information, and is valid for large antenna numbers N. In contrast to previous asymptotic methods that only focused on the distribution close to its most probable value, this methodology obtains the full distribution, including its non-Gaussian tails. The resulting distribution interpolates between the Gaussian approximation for rates R close its mean and the asymptotic distribution for large signalto-noise ratios (SNRs) ρ [1]. For large enough N, this method provides the outage probability over the whole (R, ρ) parameter space. The presented analytic results agree very well with numerical simulations over a wide range of outage probabilities, even for small N. In addition, the outage probability thus obtained is more robust over a wide range of ρ and R than either the Gaussian or the large-ρ approximations, providing an attractive alternative in calculating the probability density of the MIMO mutual information. Interestingly, this method also yields the eigenvalue density constrained in the subset where the mutual information is fixed to R for given ρ. Quite remarkably, this eigenvalue density has the form of the Marčenko-Pastur distribution with square-root singularities. © 2011 IEEE