Zobrazeno 1 - 10
of 297
pro vyhledávání: '"Lisovyy, O."'
Autor:
Lisovyy, O., Naidiuk, A.
Connection formulas relating Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed in terms of the large order asymptotics of the corresponding power series. We demonstrate that for the usual, confluent and reduced
Externí odkaz:
http://arxiv.org/abs/2208.01604
Autor:
Lisovyy, O., Naidiuk, A.
Classical Virasoro conformal blocks are believed to be directly related to accessory parameters of Floquet type in the Heun equation and some of its confluent versions. We extend this relation to another class of accessory parameter functions that ar
Externí odkaz:
http://arxiv.org/abs/2101.05715
Autor:
Gamayun, O., Lisovyy, O.
We study self-similar solutions of the binormal curvature flow which governs the evolution of vortex filaments and is equivalent to the Landau-Lifshitz equation. The corresponding dynamics is described by the real solutions of $\sigma$-Painlev\'{e} I
Externí odkaz:
http://arxiv.org/abs/1903.02105
We prove a Fredholm determinant and short-distance series representation of the Painlev\'e V tau function $\tau(t)$ associated to generic monodromy data. Using a relation of $\tau(t)$ to two different types of irregular $c=1$ Virasoro conformal block
Externí odkaz:
http://arxiv.org/abs/1806.08344
We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest example is give
Externí odkaz:
http://arxiv.org/abs/1801.09608
Publikováno v:
Commun. Math. Phys. (2019) 365: 741
We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed as the Fr
Externí odkaz:
http://arxiv.org/abs/1712.08546
Autor:
Gavrylenko, P., Lisovyy, O.
We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $\Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to th
Externí odkaz:
http://arxiv.org/abs/1705.01869
Autor:
Lisovyy, O., Roussillon, J.
Publikováno v:
J. Phys. A: Math. Theor. 50 (2017) 255202
We study the dependence of the tau function of Painlev\'e I equation on the generalized monodromy of the associated linear problem. In particular, we compute connection constants relating the tau function asymptotics on five canonical rays at infinit
Externí odkaz:
http://arxiv.org/abs/1612.08382
Autor:
Gavrylenko, P., Lisovyy, O.
Publikováno v:
Commun. Math. Phys. 363, No. 1, (2018), 1-58
We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with $n$ regular singular points on the Riemann sphere and generic monodromy in $\mathrm{GL}(N,\mathbb C)$. The corresponding operator acts in the direc
Externí odkaz:
http://arxiv.org/abs/1608.00958
Publikováno v:
Duke Math. J. 167, no. 7 (2018), 1347-1432
We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results o
Externí odkaz:
http://arxiv.org/abs/1604.03082