Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

Krylov complexity measures operator growth with respect to a basis, which is adapted to the
Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm …

This is the first book on constructive methods for, and applications of orthogonal
polynomials, and the first available collection of relevant Matlab codes. The book begins …

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A bstract We study a precise and computationally tractable notion of operator complexity in
holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and …

We study the characteristic polynomial pn (x)=∏ j= 1 n (| zj|-x) where the zj are drawn from
the Mittag–Leffler ensemble, ie a two-dimensional determinantal point process which …

Complex Jacobi matrices play an important role in the study of asymptotics and zero
distribution of formal orthogonal polynomials (FOPs). The latter are essential tools in several …

This paper deals with the general theory of sets of polynomials verifying a (d+ 1)-order
recurrence. The case d= 2 is specially carried out. First, we introduce the notion of …

We address the computational spectral theory of Jacobi operators that are compact
perturbations of the free Jacobi operator via the asymptotic properties of a connection …

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued
fraction expansions is summarized and an attempt is made to describe the influence of …