Toeplitz operators and random matrices : in memory of Harold Widom 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a biography of Harold Widom personal notes written by his former students or colleagues and also his last previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widoms 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 to Widoms work. Part I Harold Widom’s Life Work and Last Paper Biography of Harold Widom Domain Walls in the Heisenberg Ising Spin 1 2 Chain Harold Widom’s Contributions to the Spectral Theory and Asymptotics of Toeplitz Operators and Matrices Visualizations of Two Functions Emerging in Connection with Toeplitz Determinants Part II Personal Notes A Remarkable Advisor Mentor and Friend My Encounters with Harold Widom Memories of Harold Widom Personal Reflection on Harold Widom Part III Invited Contributions Loops in SU (2) and Factorization II Openness of Regular Regimes of Complex Random Matrix Models Focusing Nonlocal Nonlinear Schrödinger Equation with Asymmetric Boundary Conditions: Large Time Behavior Algebras of Commuting Differential Operators for Kernels of Airy Type A Random Walk on the Rado Graph Widom Factors and Szeg˝o–Widom Asymptotics a Review Some Recent Progress on the Stationary Measure for the Open KPZ Equation Probability of Two Large Gaps in the Bulk and at the Edge of the Spectrum of Random Matrices Multiplicative Properties of Infinite Block Toeplitz and Hankel Matrices Toeplitz and Related Operators on Polyanalytic Fock Spaces Strong Szeg˝o Theorem on a Jordan Curve Toeplitz Operators with Non trivial Kernels and Non dense Ranges on Weak Hardy Spaces Rényi Entropies of the Free Fermi Gas in Multi Dimensional Space at High Temperature Spectral Asymptotics for Toeplitz Matrices Having Certain Piecewise Continuous Symbols Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi β Ensembles On the Limit of Some Variable Coefficient Toeplitz Like Determinants On Diagonalizable Quantum Weighted Hankel Matrices On the Product Formula for Toeplitz and Related Operators.