相关论文: Matrix Models as Integrable Systems

Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…

Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…

Following Natanzon-Zabrodin, we explore the Kadomtsev-Petviashvili hierarchy as an infinite system of mutually consistent relations on the second derivatives of the free energy with some universal coefficients. From this point of view,…

Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…

We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…

This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a…

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…

We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…

An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.

Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…

We suggest a two-matrix model depending on three (infinite) sets of parameters which interpolates between all the models proposed in arXiv:2206.13038, and defined there through $W$-representations. We also discuss further generalizations of…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…

First we introduce the two tau-functions which appeared either as the $\tau$-function of the integrable hierarchy governing the Riemann mapping of Jordan curves or in conformal field theory and the universal Grassmannian. Then we discuss…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.