Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Deaño, Alfredo"'
We describe the pole-free regions of the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlev\'e equation, constructed from the Airy functions. This is achieved by exploiting the connection between these solutions and the
Externí odkaz:
http://arxiv.org/abs/2403.03023
Publikováno v:
JSTAT 013105 (2024)
We characterize the long-term state of the 1D Dirac vacuum stirred by an impenetrable object, modeled as the ground state of a finite free-fermionic chain dynamically perturbed by a moving classical obstacle which suppresses the local hopping amplitu
Externí odkaz:
http://arxiv.org/abs/2310.16693
We show that the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlev\'e equation, constructed from the Airy functions, as well as associated solutions of P$_\mathrm{XXXIV}$ and S$_\mathrm{II}$, can be expressed via the re
Externí odkaz:
http://arxiv.org/abs/2310.14898
In this paper, we study parameter deformations of matrix valued orthogonal polynomials (MVOPs). These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by
Externí odkaz:
http://arxiv.org/abs/2302.14789
Autor:
Deaño, Alfredo
In this paper, we revisit large variable asymptotic expansions of tronqu\'ee solutions of the Painlev\'e I equation, obtained via the Riemann-Hilbert approach and the method of steepest descent. The explicit construction of an extra local parametrix
Externí odkaz:
http://arxiv.org/abs/2301.11188
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou method of ste
Externí odkaz:
http://arxiv.org/abs/2210.00797
Publikováno v:
J. Math. Phys., 63, Paper No. 063303, 2022
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 in our previous paper, the whole phase space of the model, $t\in\mathbb
Externí odkaz:
http://arxiv.org/abs/2201.12871
We study a family of monic orthogonal polynomials which are orthogonal with respect to the varying, complex valued weight function, $\exp(nsz)$, over the interval $[-1,1]$, where $s\in\mathbb{C}$ is arbitrary. This family of polynomials originally ap
Externí odkaz:
http://arxiv.org/abs/2008.08724
Autor:
Deaño, Alfredo, Simm, Nick
Publikováno v:
International Mathematics Research Notices, rnaa111 (2020)
We study expectations of powers and correlation functions for characteristic polynomials of $N \times N$ non-Hermitian random matrices. For the $1$-point and $2$-point correlation function, we obtain several characterizations in terms of Painlev\'e t
Externí odkaz:
http://arxiv.org/abs/1909.06334
Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on $\mathbb{R}$, and we derive algebraic and differential rela
Externí odkaz:
http://arxiv.org/abs/1907.07447