Scalar Product of the Five-Vertex Model and Complete Symmetric Polynomials

Scalar Product of the Five-Vertex Model and Complete Symmetric Polynomials

The scalar product of the state-vectors of the exactly solvable five-vertex model with the fixed boundary conditions is considered. Various relations including those in terms of complete symmetric polynomials are derived. The limiting forms of the obtained answers may be interpreted in terms of rand...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.284 (5), p.654-664
Hauptverfasser: Bogoliubov, N. M., Malyshev, C. L.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Mathematics
Mathematics and Statistics
Polynomials
Random walk
State vectors
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Zusammenfassung:The scalar product of the state-vectors of the exactly solvable five-vertex model with the fixed boundary conditions is considered. Various relations including those in terms of complete symmetric polynomials are derived. The limiting forms of the obtained answers may be interpreted in terms of random walks on a square grid.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07376-7