M. Yattselev

activity

20082026

most citedPade approximants for functions with branch points - strong asymptotics of Nuttall-Stahl polynomials

51 citations · 98 across the 40 of their papers we have counts for

collaborators

44 papers

math.CA2026

On AAA approximants on an interval to Nevanlinna-Pick functions and Pólya Frequency Series

Sergey A. Denisov, Maxim L. Yattselev

We study the connection between AAA (triple A) algorithm and multi-point Padé approximation when the approximated functions belong to either the Nevanlinna-Pick class or are Pólya…

math.CA2026

Asymptotics of Polynomials Orthogonal on an Interval with Varying Weights

Sergey A. Denisov, Maxim L. Yattselev

We study strong asymptotics of orthogonal polynomials on an interval with varying weights, extending the framework of Totik's theorem on weighted orthogonal polynomials. Our result…

nlin.SI2026

Transition asymptotics for the real solutions of the sinh-Gordon Painlevé III equation

Kenta Miyahara, Maxim L. Yattselev

We consider solutions of the sinh-Gordon Painlevé III equation \[ u_{xx} + \frac{1}{x} u_x = \sinh u \] that are real on $(0, \infty)$ . They are parametrized by the monodromy parame…

math-ph2026

Long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field Revisited

Noah Hout, Kenta Miyahara, Dustin Newland +1

Following the work of Deift and Zhou (DOI:10.1007/978-1-4615-2474-8_15), we analyze the long-time asymptotics of the autocorrelation function of the transverse Ising chain at the c…

nlin.PS2025

Soliton Synchronization with Randomness: Rogue Waves and Universality

Manuela Girotti, Tamara Grava, Robert Jenkins +3

We consider an $N$ -soliton solution of the focusing nonlinear Schrödinger equations. We give conditions for the synchronous collision of these $N$ solitons. When the solitons veloc…

math.CA2024

Uniformity of Strong Asymptotics in Angelesco Systems

Maxim L. Yattselev

Let $μ_{1}$ and $μ_{2}$ be two complex-valued Borel measures on the real line such that $supp μ_{1} = [α_{1}, β_{1}] < supp μ_{2} = [α_{2}, β_{2}]$ and ${\rm d}μ_i(x) = -…

nlin.SI2024

The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation

Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev

Motivated by the simplest case of tt*-Toda equations, we study the large and small $x$ asymptotics for $x > 0$ of real solutions of the sinh-Godron Painlevé III( $D_{6}$ ) equation. Thes…

math-ph2024

On Airy solutions of P $_{II}$ and the complex cubic ensemble of random matrices, II

Ahmad Barhoumi, Pavel Bleher, Alfredo Deaño +1

We describe the pole-free regions of the one-parameter family of special solutions of P $_{II}$ , the second Painlevé equation, constructed from the Airy functions. This is ac…

math.CA2024

On an identity by Ercolani, Lega, and Tippings

Maxim L. Yattselev

In this note we prove that \[ j!\,2^N \, \binom{N+j-1}{j} \, {}_2F_1\left(\begin{matrix}-j,-2j \\ -N-j+1 \end{matrix};-1\right) = \sum_{l=0}^N \binom{N}{l}\prod_{i=0}^{j-1}2(2i+1+l…

math-ph2023

On Airy Solutions of P $_{II}$ and Complex Cubic Ensemble of Random Matrices, I

Ahmad Barhoumi, Pavel Bleher, Alfredo Deaño +1

We show that the one-parameter family of special solutions of P $_{II}$ , the second Painlevé equation, constructed from the Airy functions, as well as associated solutions of…

math.CA2023

Non-Hermitian Orthogonal Polynomials on a Trefoil

Ahmad B. Barhoumi, Maxim L. Yattselev

We investigate asymptotic behavior of polynomials $Q_{n} (z)$ satisfying non-Hermitian orthogonality relations $\int_{Δ} s^{k} Q_{n} (s) ρ (s) d s = 0, k \in {0, \dots, n - 1},$ where $Δ$ …

math.CA2022

On Smooth Perturbations of Chebyshëv Polynomials and $\partial ˉ$ -Riemann-Hilbert Method

Maxim L. Yattselev

$\partial ˉ$ -extension of the matrix Riemann-Hilbert method is used to study asymptotics of the polynomials $P_{n} (z)$ satisfying orthogonality relations \[ \int_{-1}^1 x^lP_n(x)\f…

math.CA2022

On $L_{R}^{2}$ -best rational approximants to Markov functions on several intervals

Maxim L. Yattselev

Let $f (z) = \int (z - x)^{- 1} d μ (x)$ , where $μ$ is a Borel measure supported on several subintervals of $(- 1, 1)$ with smooth Radon-Nikodym derivative. We study strong asymptotic beh…

math-ph2022

Investigation of the two-cut phase region in the complex cubic ensemble of random matrices

Ahmad Barhoumi, Pavel M. Bleher, Alfredo Deaño +1

We investigate the phase diagram of the complex cubic unitary ensemble of random matrices with the potential $V (M) = - \frac{1}{3} M^{3} + tM$ where $t$ is a complex parameter. As proven i…

math.CA2021

On multipoint Padé approximants whose poles accumulate on contours that separate the plane

M. L. Yattselev

In this note we consider asymptotics of the multipoint Padé approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting $- 1$ and $1$ …

math.CA2021★ 1 cited

Convergence of two-point Padé approximants to piecewise holomorphic functions

M. L. Yattselev

Let $f_{0}$ and $f_{\infty}$ be formal power series at the origin and infinity, and $P_{n} / Q_{n}$ , with $deg (P_{n}), deg (Q_{n}) \leq n$ , be a rational function that sim…

math.PR2020

An asymptotic expansion for the expected number of real zeros of Kac-Geronimus polynomials

Hanan Aljubran, Maxim L. Yattselev

Let ${φ_{i} (z; α)}_{i = 0}^{\infty}$ , corresponding to $α \in (- 1, 1)$ , be orthonormal Geronimus polynomials. We study asymptotic behavior of the expected number of real zeros, say $ \…

math.CA2020

Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality

Sergey A. Denisov, Maxim L. Yattselev

We study Jacobi matrices on trees whose coefficients are generated by multiple orthogonal polynomials. Hilbert space decomposition into an orthogonal sum of cyclic subspaces is obt…

math.SP2020

Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum

Alexander I. Aptekarev, Sergey A. Denisov, Maxim L. Yattselev

We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was discovered previously by the authors. In this pape…

math.CA2019

Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight

Ahmad Barhoumi, Maxim L. Yattselev

We investigate asymptotic behavior of polynomials $Q_{n} (z)$ satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $…

math.CA2018

An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC

Hanan Aljubran, Maxim L. Yattselev

Let ${φ_{i}}_{i = 0}^{\infty}$ be a sequence of orthonormal polynomials on the unit circle with respect to a positive Borel measure $μ$ that is symmetric with respect to conjugation…

math.CA2018

Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials

Alexander I. Aptekarev, Sergey A. Denisov, Maxim L. Yattselev

We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions…

math.CA2018

The reciprocal Mahler ensembles of random polynomials

Christopher D. Sinclair, Maxim L. Yattselev

We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree $N$ whose Mahler measure is bounded by a constant. After a change of variables this redu…

math.CA2017

Zeros of real random polynomials spanned by OPUC

Maxim L. Yattselev, Aaron Yeager

Let $ \{φ_i\}_{i=0}^\infty $ be a sequence of orthonormal polynomials on the unit circle with respect to a probability measure $ μ$. We study zero distribution of random linear…

On AAA approximants on an interval to Nevanlinna-Pick functions and Pólya Frequency Series

Asymptotics of Polynomials Orthogonal on an Interval with Varying Weights

Transition asymptotics for the real solutions of the sinh-Gordon Painlevé III equation

Long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field Revisited

Soliton Synchronization with Randomness: Rogue Waves and Universality

Uniformity of Strong Asymptotics in Angelesco Systems

The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation

On Airy solutions of PII​ and the complex cubic ensemble of random matrices, II

On an identity by Ercolani, Lega, and Tippings

On Airy Solutions of PII​ and Complex Cubic Ensemble of Random Matrices, I

Non-Hermitian Orthogonal Polynomials on a Trefoil

On Smooth Perturbations of Chebyshëv Polynomials and ∂ˉ-Riemann-Hilbert Method

On LR2​-best rational approximants to Markov functions on several intervals

Investigation of the two-cut phase region in the complex cubic ensemble of random matrices

On multipoint Padé approximants whose poles accumulate on contours that separate the plane

Convergence of two-point Padé approximants to piecewise holomorphic functions

An asymptotic expansion for the expected number of real zeros of Kac-Geronimus polynomials

Spectral theory of Jacobi matrices on trees whose coefficients are generated by multiple orthogonality

Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum

Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight

An asymptotic expansion for the expected number of real zeros of real random polynomials spanned by OPUC

Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials

The reciprocal Mahler ensembles of random polynomials

Zeros of real random polynomials spanned by OPUC

On Airy solutions of P $_{II}$ and the complex cubic ensemble of random matrices, II

On Airy Solutions of P $_{II}$ and Complex Cubic Ensemble of Random Matrices, I

On Smooth Perturbations of Chebyshëv Polynomials and $\partial ˉ$ -Riemann-Hilbert Method

On $L_{R}^{2}$ -best rational approximants to Markov functions on several intervals