Bailey R. Groups and Graphs, Designs and Dynamics 2024

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Bailey R. Groups and Graphs, Designs and Dynamics 2024

Textbook in PDF format This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references. Preface Topics in representation theory of finite groups Quantum probability approach to spectral analysis of growing graphs Laplacian eigenvalues and optimality Symbolic dynamics and the stable algebra of matrices Author Index Subject Index