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math-phSep 16, 2023
authors
  • I. M. Loutsenko
  • V. P. Spiridonov
  • O. V. Yermolayeva
institutions
  • Joint Institute for Nuclear Research
  • National Research University Higher School of Economics
  • Université de Montréal
arXiv abstractPDF
paper

Solitons and Normal Random Matrices

arXiv:2309.09016 · doi:10.1088/1742-5468/ad002f

Abstract

We discuss a general relation between the solitons and statistical mechanics and show that the partition function of the normal random matrix model can be obtained from the multi-soliton solutions of the two-dimensional Toda lattice hierarchy in a special limit.

References in corpus (13)

  • Integrable Hierarchies and Dispersionless Limit
  • Integrable Structure of Interface Dynamics
  • Universal Superpositions of Coherent States and Self-Similar Potentials
  • On the structure of Normal Matrix Model
  • Toda hierarchies and their applications
  • Random Matrices in 2D, Laplacian Growth and Operator Theory
  • Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions
  • On Products of Random Matrices
  • Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics
  • Fermionic approach to the evaluation of integrals of rational symmetric functions
  • A Critical Phenomenon in Solitonic Ising Chains
  • On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
  • New solvable matrix models III
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