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

Author: Svante Janson
Publisher: American Mathematical Soc.
ISBN: 082182595X
Category : Mathematics
Languages : en
Pages : 90

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Book Description
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.

Author: Michael Drmota
Publisher: Birkhäuser
ISBN: 3034879156
Category : Computers
Languages : en
Pages : 542

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Book Description
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.

Author: Svante Janson
Publisher: Cambridge University Press
ISBN: 0521561280
Category : Mathematics
Languages : en
Pages : 358

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Book Description
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.

Author: A. L. Levin
Publisher: American Mathematical Soc.
ISBN: 0821825992
Category : Mathematics
Languages : en
Pages : 166

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Book Description
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.

Author: Chris Jantzen
Publisher: American Mathematical Soc.
ISBN: 0821804820
Category : Mathematics
Languages : en
Pages : 114

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Book Description
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.

Author: Friedrich Tomi
Publisher: American Mathematical Soc.
ISBN: 0821803522
Category : Mathematics
Languages : en
Pages : 90

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Book Description
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.

Author: Hongbing Su
Publisher: American Mathematical Soc.
ISBN: 0821826077
Category : Mathematics
Languages : en
Pages : 98

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Book Description
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.

Author: Tomás Feder
Publisher: American Mathematical Soc.
ISBN: 0821803476
Category : Computers
Languages : en
Pages : 242

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Book Description
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.

Author: Stéphane Jaffard
Publisher: American Mathematical Soc.
ISBN: 0821804758
Category : Mathematics
Languages : en
Pages : 127

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Book Description
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.

Author: Dihua Jiang
Publisher: American Mathematical Soc.
ISBN: 0821804766
Category : Mathematics
Languages : en
Pages : 210

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Book Description
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.