3 papers
math-ph2025
Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general -Painlevé III tau functions
Pavlo Gavrylenko
We reformulate the -difference linear system corresponding to the -Painlevé equation of type as a Riemann-Hilbert problem on a circle. Then, we consider the Fred…
math-ph2020
Irregular conformal blocks, Painlevé III and the blow-up equations
Pavlo Gavrylenko, Andrei Marshakov, Artem Stoyan
We study the relation of irregular conformal blocks with the Painlevé III equation. The functional representation for the quasiclassical irregular block is shown to be consiste…
math-ph2018
Crossing invariant correlation functions at from isomonodromic functions
Pavlo Gavrylenko, Raoul Santachiara
We present an approach that gives rigorous construction of a class of crossing invariant functions in CFTs from the weakly invariant distributions on the moduli space $\mathc…