Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics
Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics

Author: Svante Janson

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 90

ISBN-13: 082182595X

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We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.

Mathematics and Computer Science III
Mathematics and Computer Science III

Author: Michael Drmota

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 542

ISBN-13: 3034879156

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Mathematics and Computer Science III contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the Third International Colloquium on Mathematics and Computer Science, held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers.

Gaussian Hilbert Spaces
Gaussian Hilbert Spaces

Author: Svante Janson

Publisher: Cambridge University Press

Published: 1997-06-12

Total Pages: 358

ISBN-13: 0521561280

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This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and theoretical physics. The emphasis throughout this book is on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.

Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$

Author: A. L. Levin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 166

ISBN-13: 0821825992

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Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups
Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups

Author: Chris Jantzen

Publisher: American Mathematical Soc.

Published: 1996-01-01

Total Pages: 114

ISBN-13: 0821804820

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This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.

The Index Theorem for Minimal Surfaces of Higher Genus
The Index Theorem for Minimal Surfaces of Higher Genus

Author: Friedrich Tomi

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 90

ISBN-13: 0821803522

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In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.

On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs
On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs

Author: Hongbing Su

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 98

ISBN-13: 0821826077

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In this paper a [italic capital]K-theoretic classification is given of the real rank zero [italic capital]C*-algebras that can be expressed as inductive limits of sequences of finite direct sums of matrix algebras over finite connected graphs (possibly with multiple vertices). The special case that the graphs are circles is due to Elliott.

Stable Networks and Product Graphs
Stable Networks and Product Graphs

Author: Tomás Feder

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 242

ISBN-13: 0821803476

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The structural and algorithmic study of stability in nonexpansive networks is based on a representation of the possible assignments of Boolean values for a network as vertices in a Boolean hypercube under the associated Hamming metric. This global view takes advantage of the median properties of the hypercube, and extends to metric networks, where individual values are now chosen from the finite metric spaces and combined by means of an additive product operation. The relationship between products of metric spaces and products of graphs then establishes a connection between isometric representation in graphs and nonexpansiveness in metric networks.

Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions

Author: Stéphane Jaffard

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 127

ISBN-13: 0821804758

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We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Littlewood-Paley decomposition or on the wavelet transform. We give characterizations and the main properties of these two-microlocal spaces and we give several applications, such as bounds on the dimension of the set of Hölder singularities of a function, Sobolev regularity of trace functions, and chirp expansions of specific functions.

Degree 16 Standard L-function of $GSp(2) \times GSp(2)$
Degree 16 Standard L-function of $GSp(2) \times GSp(2)$

Author: Dihua Jiang

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 210

ISBN-13: 0821804766

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Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.