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Toeplitz Operators and Random Matrices

In Memory of Harold Widom

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  • © 2022

Overview

Editors:
  1. Estelle Basor

    1. American Institute of Mathematics, Palo Alto, USA

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  2. Albrecht Böttcher

    1. Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

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  3. Torsten Ehrhardt

    1. Department of Mathematics, University of California, Santa Cruz, USA

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  4. Craig A. Tracy

    1. Department of Mathematics, University of California Davis, Davis, USA

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  • Unique collection of personal reminiscences and tributes devoted to various aspects Harold Widom's work
  • Contributions by world-wide leading experts
  • Expository and research papers on Toeplitz operators and random matrices

Part of the book series: Operator Theory: Advances and Applications (OT, volume 289)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-ix
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  2. Harold Widom’s Life, Work, and Last Paper

    1. Front Matter

      Pages 1-1
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    2. Biography of Harold Widom

      • Estelle Basor, Albrecht Böttcher, Torsten Ehrhardt, Craig A. Tracy
      Pages 3-7

    3. Domain Walls in the Heisenberg-Ising Spin-\(\frac {1}{2}\) Chain

      • Axel Saenz, Craig A. Tracy, Harold Widom
      Pages 9-47

    4. Harold Widom’s Contributions to the Spectral Theory and Asymptotics of Toeplitz Operators and Matrices

      • Estelle Basor, Albrecht Böttcher, Torsten Ehrhardt
      Pages 49-74

    5. Visualizations of Two Functions Emerging in Connection with Toeplitz Determinants

      • Elias Wegert
      Pages 75-80

  3. Personal Notes

    1. Front Matter

      Pages 81-81
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    2. A Remarkable Advisor, Mentor, and Friend

      • Estelle Basor
      Pages 83-86

    3. My Encounters with Harold Widom

      • Albrecht Böttcher
      Pages 87-99

    4. Memories of Harold Widom

      • Richard A. Libby
      Pages 101-107

    5. Personal Reflection on Harold Widom

      • Bin Shao
      Pages 109-113

  4. Invited Contributions

    1. Front Matter

      Pages 109-109
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    2. Loops in SU(2) and Factorization, II

      • Estelle Basor, Doug Pickrell
      Pages 117-149

    3. Openness of Regular Regimes of Complex Random Matrix Models

      • Marco Bertola, Pavel Bleher, Roozbeh Gharakhloo, Kenneth T. -R. McLaughlin, Alexander Tovbis
      Pages 151-192

    4. Focusing Nonlocal Nonlinear Schrödinger Equation with Asymmetric Boundary Conditions: Large-Time Behavior

      • Anne Boutet de Monvel, Yan Rybalko, Dmitry Shepelsky
      Pages 193-227

    5. Algebras of Commuting Differential Operators for Kernels of Airy Type

      • W. Riley Casper, F. Alberto Grünbaum, Milen Yakimov, Ignacio Zurrián
      Pages 229-256

    6. A Random Walk on the Rado Graph

      • Sourav Chatterjee, Persi Diaconis, Laurent Miclo
      Pages 257-299

    7. Widom Factors and Szegő–Widom Asymptotics, a Review

      • Jacob S. Christiansen, Barry Simon, Maxim Zinchenko
      Pages 301-319

    8. Some Recent Progress on the Stationary Measure for the Open KPZ Equation

      • Ivan Corwin
      Pages 321-360

    9. Probability of Two Large Gaps in the Bulk and at the Edge of the Spectrum of Random Matrices

      • B. Fahs, I. Krasovsky, T. -H. Maroudas
      Pages 361-369
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Keywords

About this book

This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. 

It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. 


The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related toWidom's work.

Editors and Affiliations

  • American Institute of Mathematics, Palo Alto, USA

    Estelle Basor

  • Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

    Albrecht Böttcher

  • Department of Mathematics, University of California, Santa Cruz, USA

    Torsten Ehrhardt

  • Department of Mathematics, University of California Davis, Davis, USA

    Craig A. Tracy

About the editors

Estelle Basor is professor emeritus of mathematics at the California Polytechnic State University, and deputy director of the American Institute of Mathematics. Her areas of research are in operator theory and the theory of random matrices.
Albrecht Böttcher is professor at TU Chemnitz. He is an author of several books and has edited a number of recent books in the Operator Theory series.


Torsten Erhardt is a professor at the UC Santa Cruz. His research interests range from functional analysis over harmonic analysis and Wiener-Hopf factorization theory to complex analysis.
 
Craig A. Tracy is emeritus distinguished professor at UC Davis. His fields of research include statistical physics, integrable systems, and probability theory.

Bibliographic Information

  • Book Title: Toeplitz Operators and Random Matrices

  • Book Subtitle: In Memory of Harold Widom

  • Editors: Estelle Basor, Albrecht Böttcher, Torsten Ehrhardt, Craig A. Tracy

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-031-13851-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-13850-8Published: 02 January 2023

  • Softcover ISBN: 978-3-031-13853-9Published: 03 January 2024

  • eBook ISBN: 978-3-031-13851-5Published: 01 January 2023

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: IX, 616

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Operator Theory

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