On Exact Evaluation of Path Integrals

Some mistakes have been correcte

Convergence of Gradient Descent for Low-Rank Matrix Approximation

This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space

Charge Screening in the Finite Temperature Schwinger Model

We compute the effective action and correlators of the Polyakov loop operator in the Schwinger model at finite temperature and discuss the realization of the discrete symmetries that occur there. We show that, due to nonlocal effects of massless fermions in two spacetime dimensions, the discrete symmetry which governs the screening of charges is spontaneously broken even in an effective one-dimensional model, when the volume is infinite. In this limit, the thermal state of the Schwinger model screens an arbitrary external charge; consequently the model is in the deconfined phase, with the charge of the deconfined fermions completely screened. In a finite volume we show that the Schwinger model is always confining.Comment: 27 pages, latex, no figures. References addded and some misprints correcte

Cohomological Partition Functions for a Class of Bosonic Theories

We argue, that for a general class of nontrivial bosonic theories the path integral can be related to an equivariant generalization of conventional characteristic classes.Comment: 9 pages; standard LATEX fil

Statistical Analysis of Path Losses for Sectorized Wireless Networks

© 1972-2012 IEEE. In modern mobile communication networks, such as 3G and 4G networks, sectorized antennas have been widely used to divide each cell into multiple sectors in order to improve coverage, spectrum efficiency, and quality of service. Large-scale path loss from a transmitting antenna to a receiving antenna should include: 1) propagation attenuation that depends on transmission distance; 2) shadowing that depends on surrounding environment; and 3) antenna loss that depends on a sectorized antenna pattern and transmission angle. An in-depth analysis of statistical characteristics of large-scale path losses involving with these three factors is crucial for the design, operation, evaluation, and optimization of modern sectorized wireless networks. In this paper, a sectorized antenna pattern is, for the first time, considered in the derivation of a closed-form expression of a probability density function (pdf) of large-scale path losses. Specifically, we first discover that the normalized pdf of propagation attenuation plus shadowing, which can be approximated by the Gaussian mixture model (GMM) with all system parameters, is fully determined by our newly defined metric 10/ln 10β/σs, namely, the attenuation exponent β to standard deviation of shadowing σs ratio (ASR). The convolution of GMM and antenna loss statistics is elaborately transformed to a series of differential equations. A closed-form pdf of large-scale path losses with sectorized antenna pattern can be obtained by solving these differential equations. To reduce the computational complexity, we further prove that the exciting sources of these differential equations can be tightly approximated by weighted Gaussian functions, and thus, the final solutions (i.e., pdf of path losses) can be derived in the form of Gaussian and Dawson functions. Our analytical results are verified by extensive numerical computation and Monte Carlo simulation results, e.g., the impact of ASR on the shape of pdf of propagation attenuation plus shadowing. Compared with traditional Gaussian-fitting approach, our newly derived pdf of large-scale path losses with sectorized antenna patterns is at least two orders of magnitude more accurate in terms of Kullback-Leibler divergence under typical propagation attenuation and shadowing conditions

Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N

The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large $N$ limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two dimensional adjoint QCD in the limit where matter field masses are large.Comment: 8 pages, late