scholarly journals Tau-functions à la Dubédat and probabilities of cylindrical events for double-dimers and CLE(4)

2021 ◽  
Author(s):  
Mikhail Basok ◽  
Dmitry Chelkak
Keyword(s):  
Tau Functions

scholarly journals On tau-functions for the KdV hierarchy

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Boris Dubrovin ◽  
Di Yang ◽  
Don Zagier
Keyword(s):  
Tau Functions ◽  
Kdv Hierarchy

scholarly journals Padé approximants on Riemann surfaces and KP tau functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Marco Bertola
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Hilbert Problem ◽  
Line Bundles ◽  
Fixed Degree ◽  
Tau Function ◽  
Tau Functions ◽  
Deformation Parameters ◽  
Higher Genus ◽  
Geometric Solutions

AbstractThe paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resulting Padé-like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal sections, in a similar fashion to the ordinary orthogonal polynomial case. The second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing between two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev–Petviashvili hierarchy with respect to either deformation parameters, and a certain modification of the 2-Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro-geometric solutions.

scholarly journals Isomonodromic Tau-Functions from Liouville Conformal Blocks

2014 ◽  
Vol 336 (2) ◽  
pp. 671-694 ◽  
Author(s):  
N. Iorgov ◽  
O. Lisovyy ◽  
J. Teschner
Keyword(s):  
Conformal Blocks ◽  
Tau Functions

scholarly journals Tau Functions as Widom Constants

2018 ◽  
Vol 365 (2) ◽  
pp. 741-772 ◽  
Author(s):  
M. Cafasso ◽  
P. Gavrylenko ◽  
O. Lisovyy
Keyword(s):  
Tau Functions

scholarly journals Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions

2018 ◽  
Vol 13 (2) ◽  
pp. 235-271 ◽  
Author(s):  
Victor G. Kac ◽  
Johan W. van de Leur
Keyword(s):  
Tau Functions

scholarly journals Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials

2018 ◽  
Author(s):  
Mattia Cafasso ◽  
◽  
Ann du Crest de Villeneuve ◽  
Di Yang ◽  
◽  
...  
Keyword(s):  
Schur Polynomials ◽  
Tau Functions

scholarly journals Tau-functions and generalized intergrable hierarchies

1993 ◽  
Vol 157 (1) ◽  
pp. 99-117 ◽  
Author(s):  
Timothy Hollowood ◽  
J. Luis Miramontes
Keyword(s):  
Tau Functions

Tau Functions and their Applications

2021 ◽  
Author(s):  
John Harnad ◽  
Ferenc Balogh
Keyword(s):  
Tau Functions
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