Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (2): 405-419.doi: 10.1007/s10473-024-0201-4

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FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY

Ang FU, Mingjin LI, Di YANG*   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • Received:2022-11-11 Revised:2023-07-16 Online:2024-04-25 Published:2023-12-06
  • Contact: *Di YANG, E-mail: diyang@ustc.edu.cn
  • About author:Ang FU, E-mail: fuang@mail.ustc.edu.cn; Mingjin LI, E-mail: lmj19080@mail.ustc.edu.cn
  • Supported by:
    National Key R and D Program of China (2020YFA0713100).

Abstract: For an arbitrary solution to the Volterra lattice hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method. In this paper, we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent; based on this we obtain a new formula for the $k$-point functions for the Volterra lattice hierarchy in terms of wave functions. As an application, we give an explicit formula of $k$-point functions for the even GUE (Gaussian Unitary Ensemble) correlators.

Key words: Volterra lattice hierarchy, matrix-resolvent method, wave functions, even GUE correlators

CLC Number: 

  • 37K10
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