Zobrazeno 1 - 10
of 186
pro vyhledávání: '"Bertola, Marco"'
Autor:
Bertola, Marco
We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in special cases, provide solutions of (generalized) Chebotarov problem as
Externí odkaz:
http://arxiv.org/abs/2408.15234
We develop the theory of integrable operators $\mathcal{K}$ acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is
Externí odkaz:
http://arxiv.org/abs/2307.13119
Publikováno v:
SIGMA 19 (2023), 104, 22 pages
We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szeg\H{o} kernel on the spectral curve. Using variational formulas for the
Externí odkaz:
http://arxiv.org/abs/2303.05602
We study the WKB expansion of $2\times 2$ system of linear differential equations with four fuchsian singularities. The main focus is on the generating function of the monodromy symplectomorphism which, according to a recent paper is closely related
Externí odkaz:
http://arxiv.org/abs/2211.16615
We obtain Fredholm type formulas for partial degenerations of Theta functions on (irreducible) nodal curves of arbitrary genus, with emphasis on nodal curves of genus one. An application is the study of "many-soliton" solutions on an elliptic (cnoida
Externí odkaz:
http://arxiv.org/abs/2210.01350
Critical measures in the complex plane are saddle points for the logarithmic energy with external field. Their local and global structure was described by Martinez-Finkelshtein and Rakhmanov. In this paper we start the development of a theory of crit
Externí odkaz:
http://arxiv.org/abs/2207.02068
A famous result of Stieltjes relates the zeroes of the classical orthogonal polynomials with the configurations of points on the line that minimize a suitable energy. The energy has logarithmic interactions and an external field whose exponential is
Externí odkaz:
http://arxiv.org/abs/2206.06861
The paper addresses a conjecture of Shapiro and Tater on the similarity between two sets of points in the complex plane; on one side is the values of $t\in \mathbb{C}$ for which the spectrum of the quartic anharmonic oscillator in the complex plane $
Externí odkaz:
http://arxiv.org/abs/2203.16889
Autor:
Bertola, Marco, Bleher, Pavel, Gharakhloo, Roozbeh, McLaughlin, Kenneth T-R, Tovbis, Alexander
Consider the general complex polynomial external field $$ V(z)=\frac{z^{k}}{k}+\sum_{j=1}^{k-1} \frac{t_j z^j}{j}, \qquad t_j \in \mathbb{C}, \quad k \in \mathbb{N}. $$ Fix an equivalence class $\mathcal{T}$ of admissible contours whose members appro
Externí odkaz:
http://arxiv.org/abs/2203.11348
Autor:
Bertola, Marco, Korotkin, Dmitry
The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ for Gauss' hypergeometric functions. We define the tau-function of such a system as the generating func
Externí odkaz:
http://arxiv.org/abs/2201.01451