Displaying similar documents to “The asymptotic trace norm of random circulants and the graph energy”

The random paving property for uniformly bounded matrices

Joel A. Tropp (2008)

Studia Mathematica

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This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original...

Random procedures for dominating sets in bipartite graphs

Sarah Artmann, Jochen Harant (2010)

Discussiones Mathematicae Graph Theory

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Using multilinear functions and random procedures, new upper bounds on the domination number of a bipartite graph in terms of the cardinalities and the minimum degrees of the two colour classes are established.

Matrix and discrepancy view of generalized random and quasirandom graphs

Marianna Bolla, Ahmed Elbanna (2016)

Special Matrices

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We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies,...

Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Gyula Y. Katona, Morteza Faghani, Ali Reza Ashrafi (2014)

Discussiones Mathematicae Graph Theory

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The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

Perturbed Toeplitz operators and radial determinantal processes

Torsten Ehrhardt, Brian Rider (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.

Inverting covariance matrices

Czesław Stępniak (2006)

Discussiones Mathematicae Probability and Statistics

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Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.

Smallest singular value of sparse random matrices

Alexander E. Litvak, Omar Rivasplata (2012)

Studia Mathematica

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We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances...